This paper deals with the study of CR-submanifolds of a nearly trans-Sasakian manifold with a semi symmetric non-metric connection. Nijenhuis tensor, integrability conditions for some distributions on CR-submanifolds ...This paper deals with the study of CR-submanifolds of a nearly trans-Sasakian manifold with a semi symmetric non-metric connection. Nijenhuis tensor, integrability conditions for some distributions on CR-submanifolds of a nearly trans-Sasakian manifold with a semi symmetric non- metric connection are discussed.展开更多
In this paper, we obtain Chen’s inequalities in (k,?μ)-contact space form with a semi-symmetric non-metric connection. Also we obtain the inequalites for Ricci and K-Ricci curvatures.
This paper studies the induced Chern connection of submanifolds in a Finsler manifold and gets the relations between the induced Chern connection and the Chern connection of the induced Finsler metric. Then the author...This paper studies the induced Chern connection of submanifolds in a Finsler manifold and gets the relations between the induced Chern connection and the Chern connection of the induced Finsler metric. Then the authors point out a difference between Finsler submanifolds and Riemann submanifolds.展开更多
The idea of this research is to study different types of connections in an almost Hermite manifold. The connection has been established between linear connection and Riemannian connection. Three new linear connections...The idea of this research is to study different types of connections in an almost Hermite manifold. The connection has been established between linear connection and Riemannian connection. Three new linear connections <span style="white-space:nowrap;">∇</span><sup>1</sup>, <span style="white-space:nowrap;">∇</span><sup>2</sup>, <span style="white-space:nowrap;">∇</span><sup>3</sup> are introduced. The necessary and sufficient condition for <span style="white-space:nowrap;">∇</span><sup>1</sup>, <span style="white-space:nowrap;">∇</span><sup>2</sup>, <span style="white-space:nowrap;">∇</span><sup>3</sup> to be metric is discussed. A new metric <i>s</i><sup>*</sup> (<i>X</i>,<i>Y</i>) has been defined for (<i>M</i><sup><i>n</i></sup>,<i>F</i>,<i>g</i><sup>*</sup>) and additional properties are discussed. It is also proved that for the quarter symmetric connection <span style="white-space:nowrap;">∇ </span>is unique in given manifold. The hessian operator with respect to all connections defined above has also been discussed.展开更多
Modified Theories of Gravity include spin dependence in General Relativity, to account for additional sources of gravity instead of dark matter/energy approach. The spin-spin interaction is already included in the eff...Modified Theories of Gravity include spin dependence in General Relativity, to account for additional sources of gravity instead of dark matter/energy approach. The spin-spin interaction is already included in the effective nuclear force potential, and theoretical considerations and experimental evidence hint to the hypothesis that Gravity originates from such an interaction, under an averaging process over spin directions. This invites to continue the line of theory initiated by Einstein and Cartan, based on tetrads and spin effects modeled by connections with torsion. As a first step in this direction, the article considers a new modified Coulomb/Newton Law accounting for the spin-spin interaction. The physical potential is geometrized through specific affine connections and specific semi-Riemannian metrics, canonically associated to it, acting on a manifold or at the level of its tangent bundle. Freely falling particles in these “toy Universes” are determined, showing an interesting behavior and unexpected patterns.展开更多
Severe soil and water loss have led to widespread land degradation on the Loess Plateau in China.Exploring the relationship between land use and sediment connectivity can be beneficial to control soil erosion.In this ...Severe soil and water loss have led to widespread land degradation on the Loess Plateau in China.Exploring the relationship between land use and sediment connectivity can be beneficial to control soil erosion.In this study,three catchments in the Yanhe River Basin on the Loess Plateau were selected to analyse the relationship between land use and sediment connectivity using grey correlation method.Index of connectivity(IC)was employed to quantify sediment connectivity,including two flow direction algorithms(D8 and D-infinity)and two final targets of sediment transport(outlet and main channel of catchment).Then,11 landscape metrics were used to evaluate the land use spatial patterns of catchments.By comparing the IC value ranges,histograms and classes,and their relationship with remote sensing images of the two flow direction algorithms,we find that the D8 algorithm is more suitable for this study area.The results showed that the three catchments are characterized by high sediment connectivity in the grassland and forest close to the channel.In addition,the roads and bare land close to the channel also have high or medium sediment connectivity.Grey correlation analysis showed that landscape division index(DIVISION),fractal dimension index(FRACMN),aggregation index(AI),total class area,patch cohesion index(COHESION),and largest patch index(LPI)indices were the main factors that affect sediment connectivity at the class scale.At the landscape scale,the landscape shape index(LSI),Shannon’s diversity index(SHDI),and gully density have an essential effect on sediment connectivity.This condition provides a way to control the sediment connectivity in the watershed by transforming land use type or changing its spatial pattern,but specific adjustment measures have to be further explored.展开更多
In this article,we investigate the dynamical properties of fλ(z)=λzkez,for λ(≠0)∈C and k≥2.We will show that the boundaries of some (or all) Fatou components are Jordan curves and the Julia sets are Sierpinski c...In this article,we investigate the dynamical properties of fλ(z)=λzkez,for λ(≠0)∈C and k≥2.We will show that the boundaries of some (or all) Fatou components are Jordan curves and the Julia sets are Sierpinski carpet,and they are locally connected for some certain λ.展开更多
The authors consider a quarter-symmetric metric connection in a P-Sasakian manifold and study the second order parallel tensor in a P-Sasakian manifold with respect to the quarter-symmetric metric connection. Then Ric...The authors consider a quarter-symmetric metric connection in a P-Sasakian manifold and study the second order parallel tensor in a P-Sasakian manifold with respect to the quarter-symmetric metric connection. Then Ricci semisymmetric P-Sasakian manifold with respect to the quarter-symmetric metric connection is considered. Next the authors study ξ-concircularly flat P-Sasakian manifolds and concircularly semisymmetric P-Sasakian manifolds with respect to the quarter-symmetric metric connection. Furthermore, the authors study P-Sasakian manifolds satisfying the condition Z(ξ,Y)·S=0,where Z,S are the concircular curvature tensor and Ricci tensor respectively with respect to the quarter-symmetric metric connection. Finally, an example of a 5-dimensional P-Sasakian manifold admitting quarter-symmetric metric connection is constructed.展开更多
Let∇be a linear connection on a 2n-dimensional almost anti-Hermitian manifold M equipped with an almost complex structure J,a pseudo-Riemannian metric g and the twin metric G=g◦J.In this paper,we first introduce three...Let∇be a linear connection on a 2n-dimensional almost anti-Hermitian manifold M equipped with an almost complex structure J,a pseudo-Riemannian metric g and the twin metric G=g◦J.In this paper,we first introduce three types of conjugate connections of linear connections relative to g,G and J.We obtain a simple relation among curvature tensors of these conjugate connections.To clarify the relations of these conjugate connections,we prove a result stating that conjugations along with an identity operation together act as a Klein group,which is analogue to the known result for the Hermitian case in[2].Secondly,we give some results exhibiting occurrences of Codazzi pairs which generalize parallelism relative to∇.Under the assumption that(∇,J)being a Codazzi pair,we derive a necessary and sufficient condition the almost anti-Hermitian manifold(M,J,g,G)is an anti-K¨ahler relative to a torsion-free linear connection∇.Finally,we investigate statistical structures on M under∇(∇is a J−parallel torsion-free connection).展开更多
In this paper, we study conharmonic curvature tensor in Kenmotsu manifolds with respect to semi-symmetric metric connection and also characterize conharmonically flat, conharmonically semisymmetric and Ф-conharmonica...In this paper, we study conharmonic curvature tensor in Kenmotsu manifolds with respect to semi-symmetric metric connection and also characterize conharmonically flat, conharmonically semisymmetric and Ф-conharmonically flat Kenmotsu manifolds with respect to semi-symmetric metric connection.展开更多
文摘This paper deals with the study of CR-submanifolds of a nearly trans-Sasakian manifold with a semi symmetric non-metric connection. Nijenhuis tensor, integrability conditions for some distributions on CR-submanifolds of a nearly trans-Sasakian manifold with a semi symmetric non- metric connection are discussed.
文摘In this paper, we obtain Chen’s inequalities in (k,?μ)-contact space form with a semi-symmetric non-metric connection. Also we obtain the inequalites for Ricci and K-Ricci curvatures.
文摘This paper studies the induced Chern connection of submanifolds in a Finsler manifold and gets the relations between the induced Chern connection and the Chern connection of the induced Finsler metric. Then the authors point out a difference between Finsler submanifolds and Riemann submanifolds.
文摘The idea of this research is to study different types of connections in an almost Hermite manifold. The connection has been established between linear connection and Riemannian connection. Three new linear connections <span style="white-space:nowrap;">∇</span><sup>1</sup>, <span style="white-space:nowrap;">∇</span><sup>2</sup>, <span style="white-space:nowrap;">∇</span><sup>3</sup> are introduced. The necessary and sufficient condition for <span style="white-space:nowrap;">∇</span><sup>1</sup>, <span style="white-space:nowrap;">∇</span><sup>2</sup>, <span style="white-space:nowrap;">∇</span><sup>3</sup> to be metric is discussed. A new metric <i>s</i><sup>*</sup> (<i>X</i>,<i>Y</i>) has been defined for (<i>M</i><sup><i>n</i></sup>,<i>F</i>,<i>g</i><sup>*</sup>) and additional properties are discussed. It is also proved that for the quarter symmetric connection <span style="white-space:nowrap;">∇ </span>is unique in given manifold. The hessian operator with respect to all connections defined above has also been discussed.
文摘Modified Theories of Gravity include spin dependence in General Relativity, to account for additional sources of gravity instead of dark matter/energy approach. The spin-spin interaction is already included in the effective nuclear force potential, and theoretical considerations and experimental evidence hint to the hypothesis that Gravity originates from such an interaction, under an averaging process over spin directions. This invites to continue the line of theory initiated by Einstein and Cartan, based on tetrads and spin effects modeled by connections with torsion. As a first step in this direction, the article considers a new modified Coulomb/Newton Law accounting for the spin-spin interaction. The physical potential is geometrized through specific affine connections and specific semi-Riemannian metrics, canonically associated to it, acting on a manifold or at the level of its tangent bundle. Freely falling particles in these “toy Universes” are determined, showing an interesting behavior and unexpected patterns.
基金supported by the National Natural Science Foundation of China(42077078,U2243213)。
文摘Severe soil and water loss have led to widespread land degradation on the Loess Plateau in China.Exploring the relationship between land use and sediment connectivity can be beneficial to control soil erosion.In this study,three catchments in the Yanhe River Basin on the Loess Plateau were selected to analyse the relationship between land use and sediment connectivity using grey correlation method.Index of connectivity(IC)was employed to quantify sediment connectivity,including two flow direction algorithms(D8 and D-infinity)and two final targets of sediment transport(outlet and main channel of catchment).Then,11 landscape metrics were used to evaluate the land use spatial patterns of catchments.By comparing the IC value ranges,histograms and classes,and their relationship with remote sensing images of the two flow direction algorithms,we find that the D8 algorithm is more suitable for this study area.The results showed that the three catchments are characterized by high sediment connectivity in the grassland and forest close to the channel.In addition,the roads and bare land close to the channel also have high or medium sediment connectivity.Grey correlation analysis showed that landscape division index(DIVISION),fractal dimension index(FRACMN),aggregation index(AI),total class area,patch cohesion index(COHESION),and largest patch index(LPI)indices were the main factors that affect sediment connectivity at the class scale.At the landscape scale,the landscape shape index(LSI),Shannon’s diversity index(SHDI),and gully density have an essential effect on sediment connectivity.This condition provides a way to control the sediment connectivity in the watershed by transforming land use type or changing its spatial pattern,but specific adjustment measures have to be further explored.
基金National Natural Science Foundation of China(No.10871089)
文摘In this article,we investigate the dynamical properties of fλ(z)=λzkez,for λ(≠0)∈C and k≥2.We will show that the boundaries of some (or all) Fatou components are Jordan curves and the Julia sets are Sierpinski carpet,and they are locally connected for some certain λ.
基金supported by the National Natural Science Foundation of China(Nos.11871275,11371194).
文摘The authors consider a quarter-symmetric metric connection in a P-Sasakian manifold and study the second order parallel tensor in a P-Sasakian manifold with respect to the quarter-symmetric metric connection. Then Ricci semisymmetric P-Sasakian manifold with respect to the quarter-symmetric metric connection is considered. Next the authors study ξ-concircularly flat P-Sasakian manifolds and concircularly semisymmetric P-Sasakian manifolds with respect to the quarter-symmetric metric connection. Furthermore, the authors study P-Sasakian manifolds satisfying the condition Z(ξ,Y)·S=0,where Z,S are the concircular curvature tensor and Ricci tensor respectively with respect to the quarter-symmetric metric connection. Finally, an example of a 5-dimensional P-Sasakian manifold admitting quarter-symmetric metric connection is constructed.
文摘Let∇be a linear connection on a 2n-dimensional almost anti-Hermitian manifold M equipped with an almost complex structure J,a pseudo-Riemannian metric g and the twin metric G=g◦J.In this paper,we first introduce three types of conjugate connections of linear connections relative to g,G and J.We obtain a simple relation among curvature tensors of these conjugate connections.To clarify the relations of these conjugate connections,we prove a result stating that conjugations along with an identity operation together act as a Klein group,which is analogue to the known result for the Hermitian case in[2].Secondly,we give some results exhibiting occurrences of Codazzi pairs which generalize parallelism relative to∇.Under the assumption that(∇,J)being a Codazzi pair,we derive a necessary and sufficient condition the almost anti-Hermitian manifold(M,J,g,G)is an anti-K¨ahler relative to a torsion-free linear connection∇.Finally,we investigate statistical structures on M under∇(∇is a J−parallel torsion-free connection).
基金supported by University Grants Commission, New Delhi, India of Major Research Project(Grant No. 39-30/2010(SR))UGC, New Delhi for financial support in the form of UGC MRP
文摘In this paper, we study conharmonic curvature tensor in Kenmotsu manifolds with respect to semi-symmetric metric connection and also characterize conharmonically flat, conharmonically semisymmetric and Ф-conharmonically flat Kenmotsu manifolds with respect to semi-symmetric metric connection.