Curvature properties are studied for the Sasaki metric on the （1, 1） tensor bundle of a Riemannian manifold. As an application, examples of almost para-Nordenian and para-Kahler-Nordenian B-metrics are constructed o...Curvature properties are studied for the Sasaki metric on the （1, 1） tensor bundle of a Riemannian manifold. As an application, examples of almost para-Nordenian and para-Kahler-Nordenian B-metrics are constructed on the （1, 1） tensor bundle by looking at the Sasaki metric. Also, with respect to the para-Nordenian B-structure, paraholomorphic conditions for the complete lifts of vector fields are analyzed.展开更多
In this paper we construct a new time-periodic solution of the vacuum Einstein's field equations, this solution possesses physical singularities, i.e., the norm of the solution's Riemann curvature tensor takes...In this paper we construct a new time-periodic solution of the vacuum Einstein's field equations, this solution possesses physical singularities, i.e., the norm of the solution's Riemann curvature tensor takes the infinity at some points. We show that this solution is intrinsically time-periodic and describes a time-periodic universe with the "time-periodic physical singularity". By calculating the Weyl scalars of this solution, we investigate new physical phenomena and analyze new singularities for this universal model.展开更多
Einstein＇s equation,in its standard form,breaks down at the Big Bang singularity.A new version,equivalent to Einstein＇s whenever the latter is defined,but applicable in wider situations,is proposed.The new equation ...Einstein＇s equation,in its standard form,breaks down at the Big Bang singularity.A new version,equivalent to Einstein＇s whenever the latter is defined,but applicable in wider situations,is proposed.The new equation remains smooth at the Big Bang singularity of the Friedmann-Lemaatre-Robertson-Walker model.It is a tensor equation defined in terms of the Ricci part of the Riemann curvature.It is obtained by taking the Kulkarni-Nomizu product between Einstein＇s equation and the metric tensor.展开更多
A-manifolds and/3-manifolds, introduced by Gray （1978）, are two significant classes of Einstein-like Riemannian manifolds. A Riemannian manifold is Ricci parallel if and only if it is simultaneously an A-manifold an...A-manifolds and/3-manifolds, introduced by Gray （1978）, are two significant classes of Einstein-like Riemannian manifolds. A Riemannian manifold is Ricci parallel if and only if it is simultaneously an A-manifold and a B-manifold. The present paper proves that both focal submanifolds of each isoparametric hypersurface in unit spheres with g = 4 distinct principal curvatures are A-manifolds. As for the focal submanifolds with g = 6, m = 1 or 2, only one is an A-manifold, and neither is a B-manifold.展开更多
Both bi-harmonic maps and f-harmonic maps have some nice physical motivation and applications.Motivated largely by f-tension field not involving Riemannian curvature tensor, we attempt to formalize some large objects ...Both bi-harmonic maps and f-harmonic maps have some nice physical motivation and applications.Motivated largely by f-tension field not involving Riemannian curvature tensor, we attempt to formalize some large objects so as to broaden the notions of f-tension field and bi-tension field. We introduce a very large generalization of harmonic maps called f-bi-harmonic maps as the critical points of f-bi-energy functional, and then derive the Euler-Lagrange equation of f-bi-energy functional given by the vanishing of f-bi-tension field.Subsequently, we study some properties of f-bi-harmonic maps between the same dimensional manifolds and give a non-trivial example. Furthermore, we also study the basic properties of f-bi-harmonic maps on a warped product manifold so that we could find some interesting and complicated examples.展开更多
基金Project supported by the Scientific and Technological Research Council of Turkey(No.TBAG-108T590)
文摘Curvature properties are studied for the Sasaki metric on the （1, 1） tensor bundle of a Riemannian manifold. As an application, examples of almost para-Nordenian and para-Kahler-Nordenian B-metrics are constructed on the （1, 1） tensor bundle by looking at the Sasaki metric. Also, with respect to the para-Nordenian B-structure, paraholomorphic conditions for the complete lifts of vector fields are analyzed.
基金supported by National Natural Science Foundation of China (Grant No.10971190) and the Qiu-Shi Professor Fellowship from Zhejiang University,China
文摘In this paper we construct a new time-periodic solution of the vacuum Einstein's field equations, this solution possesses physical singularities, i.e., the norm of the solution's Riemann curvature tensor takes the infinity at some points. We show that this solution is intrinsically time-periodic and describes a time-periodic universe with the "time-periodic physical singularity". By calculating the Weyl scalars of this solution, we investigate new physical phenomena and analyze new singularities for this universal model.
文摘Einstein＇s equation,in its standard form,breaks down at the Big Bang singularity.A new version,equivalent to Einstein＇s whenever the latter is defined,but applicable in wider situations,is proposed.The new equation remains smooth at the Big Bang singularity of the Friedmann-Lemaatre-Robertson-Walker model.It is a tensor equation defined in terms of the Ricci part of the Riemann curvature.It is obtained by taking the Kulkarni-Nomizu product between Einstein＇s equation and the metric tensor.
基金supported by National Natural Science Foundation of China(Grant No.11301027)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20130003120008)+1 种基金the Beijing Natural Science Foundation(Grant No.1144013)the Fundamental Research Funds for the Central Universities(Grant No.2012CXQT09)
文摘A-manifolds and/3-manifolds, introduced by Gray （1978）, are two significant classes of Einstein-like Riemannian manifolds. A Riemannian manifold is Ricci parallel if and only if it is simultaneously an A-manifold and a B-manifold. The present paper proves that both focal submanifolds of each isoparametric hypersurface in unit spheres with g = 4 distinct principal curvatures are A-manifolds. As for the focal submanifolds with g = 6, m = 1 or 2, only one is an A-manifold, and neither is a B-manifold.
基金supported by the Science and Technology Research Project of Guangxi Universities(Grant No.2015ZD038)the Key Scientific Research Project of Guangxi University for Nationalities(Grant No.2012MDZD033)
文摘Both bi-harmonic maps and f-harmonic maps have some nice physical motivation and applications.Motivated largely by f-tension field not involving Riemannian curvature tensor, we attempt to formalize some large objects so as to broaden the notions of f-tension field and bi-tension field. We introduce a very large generalization of harmonic maps called f-bi-harmonic maps as the critical points of f-bi-energy functional, and then derive the Euler-Lagrange equation of f-bi-energy functional given by the vanishing of f-bi-tension field.Subsequently, we study some properties of f-bi-harmonic maps between the same dimensional manifolds and give a non-trivial example. Furthermore, we also study the basic properties of f-bi-harmonic maps on a warped product manifold so that we could find some interesting and complicated examples.
