In this paper,we study the compact spacelike submanifolds in the de Sitter space,under the assumption that the normalized mean curvature vector is parallel in the normal bundle.Using the generalized Cheng-Yau＇s diffe...In this paper,we study the compact spacelike submanifolds in the de Sitter space,under the assumption that the normalized mean curvature vector is parallel in the normal bundle.Using the generalized Cheng-Yau＇s differential operator,we obtain some general rigidity theorems which naturally generalize some existing results.展开更多
In Reissner-NordstrSm-de Sitter space-time, we calculate the interference phase of mass neutrino along geodesic in the radial direction, and then investigate the effects of the cosmological constant A on the phase. Mo...In Reissner-NordstrSm-de Sitter space-time, we calculate the interference phase of mass neutrino along geodesic in the radial direction, and then investigate the effects of the cosmological constant A on the phase. Morever, the expression of the interference phase can be reduced to that in Reissner-Nordstrom space-time when A approaches to zero.展开更多
Let M be an n（≥ 3）-dimensional completely non-compact spacelike hypersurface in the de Sitter space S1^n＋1 （1） with constant mean curvature and nonnegative sectional curvature. It is proved that M is isometric t...Let M be an n（≥ 3）-dimensional completely non-compact spacelike hypersurface in the de Sitter space S1^n＋1 （1） with constant mean curvature and nonnegative sectional curvature. It is proved that M is isometric to a hyperbolic cylinder or an Euclidean space if H ≥ 1. When 2√n-1/n〈 H 〈 1, there exists a complete rotation hypersurfaces which is not a hyperbolic cylinder.展开更多
A spacelike surface M in 3-dimensional de sitter space S13 or 3-dimensional anti-de Sitter space H13 is called isoparametric, if M has constant principal curvatures. A timelike surface is called isoparametric, if its ...A spacelike surface M in 3-dimensional de sitter space S13 or 3-dimensional anti-de Sitter space H13 is called isoparametric, if M has constant principal curvatures. A timelike surface is called isoparametric, if its minimal polynomial of the shape operator is constant. In this paper, we determine the spacelike isoparametric surfaces and the timelike isoparametric surfaces in S13 and H13.展开更多
The set of all spheres and hyperplanes in the Euclidean space Rn+1 could be identified with the Sitter space Λn+1. All the conformal properties are invariant by the Lorentz form which is natural pseudo-Riemannian met...The set of all spheres and hyperplanes in the Euclidean space Rn+1 could be identified with the Sitter space Λn+1. All the conformal properties are invariant by the Lorentz form which is natural pseudo-Riemannian metric on Λn+1. We shall study behaviour of some surfaces and foliations as their families using computation in the de Sitter space.展开更多
It is shown that a compact spacelike hypersurface which is contained in the chronological future (or past) of an equator of de Sitter space is a totally umbilical round sphere if the kth mean curvature function Hk is ...It is shown that a compact spacelike hypersurface which is contained in the chronological future (or past) of an equator of de Sitter space is a totally umbilical round sphere if the kth mean curvature function Hk is a linear combination of Hk+1,…, Hn. This is a new angle to characterize round spheres.展开更多
We establish integral formulas of Minkowski’s type for compact spacelike hypersurfaces in de sitter space S<sub>1</sub><sup>n+1</sup>（1）and give their applications to the case of constant r-...We establish integral formulas of Minkowski’s type for compact spacelike hypersurfaces in de sitter space S<sub>1</sub><sup>n+1</sup>（1）and give their applications to the case of constant r-th mean curvature （r=1,2,…,n-1）.When r=1 we recover Montiel’s result.展开更多
In this paper we study the cohomogeneity one de Sitter space S1 n. We consider the actions in both proper and non-proper cases. In the first case we characterize the acting groups and orbits and we prove that the orbi...In this paper we study the cohomogeneity one de Sitter space S1 n. We consider the actions in both proper and non-proper cases. In the first case we characterize the acting groups and orbits and we prove that the orbit space is homeomorphic to R. In the latter case we determine the groups and consequently the orbits in some different cases and prove that the orbit space is not Hausdorff.展开更多
The fundamental equation of the thermodynamic system gives the relation between the internal energy, entropy and volume of two adjacent equilibrium states. Taking a higher-dimensional charged Gauss–Bonnet black hole ...The fundamental equation of the thermodynamic system gives the relation between the internal energy, entropy and volume of two adjacent equilibrium states. Taking a higher-dimensional charged Gauss–Bonnet black hole in de Sitter space as a thermodynamic system, the state parameters have to meet the fundamental equation of thermodynamics. We introduce the effective thermodynamic quantities to describe the black hole in de Sitter space. Considering that in the lukewarm case the temperature of the black hole horizon is equal to that of the cosmological horizon, we conjecture that the effective temperature has the same value. In this way, we can obtain the entropy formula of spacetime by solving the differential equation. We find that the total entropy contains an extra term besides the sum of the entropies of the two horizons. The corrected term of the entropy is a function of the ratio of the black hole horizon radius to the cosmological horizon radius, and is independent of the charge of the spacetime.展开更多
Physicists have been interested in quantization of spinor and vector free fields in 4-dimensional de Sitter space-time, in ambient space notation. The Gupta-Bleuler formalism has been extensively applied to the quanti...Physicists have been interested in quantization of spinor and vector free fields in 4-dimensional de Sitter space-time, in ambient space notation. The Gupta-Bleuler formalism has been extensively applied to the quantization of gauge invariant theories. The field equation of the massless spin-3/2 fields is gauge invariant in de Sitter space. In this paper, we study the quantization of massless spin-3/2 gauge fields in de Sitter space-time by the Gupta-Bleuler formalism. This triplet carries an indecomposable representation of the de Sitter group.展开更多
Complete space-like submanifolds in a de Sitter Space with parallel mean curvature vector are investigated, a main Theorem for M to be totally umbilical is obtained.
This is a follow of previous work entitled "One Electron Atom in Special Relativity with de Sitter SpaceTime Symmetry" [Commun. Theor. Phys. 57(2012) 930]. In this paper, we consider the higher order calcula...This is a follow of previous work entitled "One Electron Atom in Special Relativity with de Sitter SpaceTime Symmetry" [Commun. Theor. Phys. 57(2012) 930]. In this paper, we consider the higher order calculations and contributions in the previous framework to solve one electron atoms in de Sitter invariant relativistic quantum mechanics. The next-to-leading-order calculations in 1/R2-expansions show that the fine-structure constant α is variant with cosmologic time going by in the de Sitter invariant special relativistic quantum mechanics with standard FRW cosmologic model.展开更多
On several levels of theoretical physics, especially particle physics and early universe cosmology, de Sitter space-time has become an attractive possibility. The principle of local gauge invariance governs all known ...On several levels of theoretical physics, especially particle physics and early universe cosmology, de Sitter space-time has become an attractive possibility. The principle of local gauge invariance governs all known fundamental interactions of elementary particles, from electromagnetism and weak interactions to strong interactions and gravity. This paper presents a procedure for defining the gauge-covariant derivative and gauge invariant Lagrangian densityin de Sitter ambient space-time formalism. The gauge invariant field equation is then explicitly calculated in detailfor a massless spit 3/2gauge field.展开更多
基金Supported by the National Natural Science Foundation of China（10561004）
文摘In this paper,we study the compact spacelike submanifolds in the de Sitter space,under the assumption that the normalized mean curvature vector is parallel in the normal bundle.Using the generalized Cheng-Yau＇s differential operator,we obtain some general rigidity theorems which naturally generalize some existing results.
基金supported by the State Key Development Program for Basic Research Program of China (Grant No.2010CB832803)the National Natural Science Foundation of China (Grant No.10873004)the Scientific Research Fund of Hunan Provincial Education Department,China (Grant No.08B051)
文摘In Reissner-NordstrSm-de Sitter space-time, we calculate the interference phase of mass neutrino along geodesic in the radial direction, and then investigate the effects of the cosmological constant A on the phase. Morever, the expression of the interference phase can be reduced to that in Reissner-Nordstrom space-time when A approaches to zero.
基金The NNSFC (10371047) and the NSF (04KJD110192) of the Education Department of Jiangsu Province, China.
文摘Let M be an n（≥ 3）-dimensional completely non-compact spacelike hypersurface in the de Sitter space S1^n＋1 （1） with constant mean curvature and nonnegative sectional curvature. It is proved that M is isometric to a hyperbolic cylinder or an Euclidean space if H ≥ 1. When 2√n-1/n〈 H 〈 1, there exists a complete rotation hypersurfaces which is not a hyperbolic cylinder.
文摘A spacelike surface M in 3-dimensional de sitter space S13 or 3-dimensional anti-de Sitter space H13 is called isoparametric, if M has constant principal curvatures. A timelike surface is called isoparametric, if its minimal polynomial of the shape operator is constant. In this paper, we determine the spacelike isoparametric surfaces and the timelike isoparametric surfaces in S13 and H13.
文摘The set of all spheres and hyperplanes in the Euclidean space Rn+1 could be identified with the Sitter space Λn+1. All the conformal properties are invariant by the Lorentz form which is natural pseudo-Riemannian metric on Λn+1. We shall study behaviour of some surfaces and foliations as their families using computation in the de Sitter space.
文摘It is shown that a compact spacelike hypersurface which is contained in the chronological future (or past) of an equator of de Sitter space is a totally umbilical round sphere if the kth mean curvature function Hk is a linear combination of Hk+1,…, Hn. This is a new angle to characterize round spheres.
基金Li Haizhong is supported by NNSFC No.19701017 Basic Science Research Foundation of Tsinghua University Chen Weihua is supported by NNSFC No.19571005
文摘We establish integral formulas of Minkowski’s type for compact spacelike hypersurfaces in de sitter space S<sub>1</sub><sup>n+1</sup>（1）and give their applications to the case of constant r-th mean curvature （r=1,2,…,n-1）.When r=1 we recover Montiel’s result.
基金Supported by Iranian Presidential Office (Grant No. 83211)
文摘In this paper we study the cohomogeneity one de Sitter space S1 n. We consider the actions in both proper and non-proper cases. In the first case we characterize the acting groups and orbits and we prove that the orbit space is homeomorphic to R. In the latter case we determine the groups and consequently the orbits in some different cases and prove that the orbit space is not Hausdorff.
基金supported by the Young Scientists Fund of the National Natural Science Foundation of China(Grant No.11205097)in part by the National Natural Science Foundation of China(Grant No.11475108)+1 种基金supported by Program for the Natural Science Foundation of Shanxi Province,China(Grant No.201901D111315)the Natural Science Foundation for Young Scientists of Shanxi Province,China(Grant No.201901D211441)。
文摘The fundamental equation of the thermodynamic system gives the relation between the internal energy, entropy and volume of two adjacent equilibrium states. Taking a higher-dimensional charged Gauss–Bonnet black hole in de Sitter space as a thermodynamic system, the state parameters have to meet the fundamental equation of thermodynamics. We introduce the effective thermodynamic quantities to describe the black hole in de Sitter space. Considering that in the lukewarm case the temperature of the black hole horizon is equal to that of the cosmological horizon, we conjecture that the effective temperature has the same value. In this way, we can obtain the entropy formula of spacetime by solving the differential equation. We find that the total entropy contains an extra term besides the sum of the entropies of the two horizons. The corrected term of the entropy is a function of the ratio of the black hole horizon radius to the cosmological horizon radius, and is independent of the charge of the spacetime.
基金supported by the Islamic Azad University,Kermanshah Branch,Kermanshah,Iran
文摘Physicists have been interested in quantization of spinor and vector free fields in 4-dimensional de Sitter space-time, in ambient space notation. The Gupta-Bleuler formalism has been extensively applied to the quantization of gauge invariant theories. The field equation of the massless spin-3/2 fields is gauge invariant in de Sitter space. In this paper, we study the quantization of massless spin-3/2 gauge fields in de Sitter space-time by the Gupta-Bleuler formalism. This triplet carries an indecomposable representation of the de Sitter group.
文摘Complete space-like submanifolds in a de Sitter Space with parallel mean curvature vector are investigated, a main Theorem for M to be totally umbilical is obtained.
基金Supported in part by National Natural Science Foundation of China under Grant No.11375169
文摘This is a follow of previous work entitled "One Electron Atom in Special Relativity with de Sitter SpaceTime Symmetry" [Commun. Theor. Phys. 57(2012) 930]. In this paper, we consider the higher order calculations and contributions in the previous framework to solve one electron atoms in de Sitter invariant relativistic quantum mechanics. The next-to-leading-order calculations in 1/R2-expansions show that the fine-structure constant α is variant with cosmologic time going by in the de Sitter invariant special relativistic quantum mechanics with standard FRW cosmologic model.
基金supported by the Islamic Azad University,Science and Research Branch,Tehran,Iran
文摘On several levels of theoretical physics, especially particle physics and early universe cosmology, de Sitter space-time has become an attractive possibility. The principle of local gauge invariance governs all known fundamental interactions of elementary particles, from electromagnetism and weak interactions to strong interactions and gravity. This paper presents a procedure for defining the gauge-covariant derivative and gauge invariant Lagrangian densityin de Sitter ambient space-time formalism. The gauge invariant field equation is then explicitly calculated in detailfor a massless spit 3/2gauge field.
