One of the fundamental problems in Finsler geometry is to study Finsler metrics of constant(or scalar)curvature.In this paper,we refine and improve Chen-Shen-Zhao equations characterizing Finsler warped product metric...One of the fundamental problems in Finsler geometry is to study Finsler metrics of constant(or scalar)curvature.In this paper,we refine and improve Chen-Shen-Zhao equations characterizing Finsler warped product metrics of scalar flag curvature.In particular,we find equations that characterize Finsler warped product metrics of constant flag curvature.Then we improve the Chen-Shen-Zhao result on characterizing Einstein Finsler warped product metrics.As its application we construct explicitly many new warped product Douglas metrics of constant Ricci curvature by using known locally projectively flat spherically symmetric metrics of constant flag curvature.展开更多
Doubly warped product of Finsler manifolds is useful in theoretical physics,particularly in general relativity.In this paper,we study doubly warped product of Finsler manifolds with isotropic mean Berwald curvature or...Doubly warped product of Finsler manifolds is useful in theoretical physics,particularly in general relativity.In this paper,we study doubly warped product of Finsler manifolds with isotropic mean Berwald curvature or weak isotropic S-curvature.展开更多
Let （M1, F1） and （M2, F2） be two strongly pseudoconvex complex Finsler man- ifolds. The doubly wraped product complex Finsler manifold （f2 M1 x h M2, F） of （M1, F1） and （M2, F2） is the product manifold M1 x ...Let （M1, F1） and （M2, F2） be two strongly pseudoconvex complex Finsler man- ifolds. The doubly wraped product complex Finsler manifold （f2 M1 x h M2, F） of （M1, F1） and （M2, F2） is the product manifold M1 x M2 endowed with the warped product complex 2 2 Finsler metric F2 = f2F1 ＋ fl F2, where fl and f2 are positive smooth functions on M1 and M2, respectively. In this paper, the most often used complex Finsler connections, holomorphic curvature, Ricci scalar curvature, and real geodesics of the DWP-complex Finsler manifold are derived in terms of the corresponding objects of its components. Necessary and sufficient conditions for the DWP-complex Finsler manifold to be K/ihler Finsler （resp., weakly K/ihler Finsler, complex Berwald, weakly complex Berwald, complex Landsberg） manifold are ob- tained, respectively. It is proved that if （M1, F1） and （M2,F2） are projectively flat, then the DWP-complex Finsler manifold is projectively flat if and only if fl and f2 are positive constants.展开更多
Based on the Mach’s principle, black holes warp the space time in a way that geodesic for every object which is moving toward black hole starts to bend and object starts to rotate around the black hole. Even light ca...Based on the Mach’s principle, black holes warp the space time in a way that geodesic for every object which is moving toward black hole starts to bend and object starts to rotate around the black hole. Even light cannot be able to escape from the strong gravitational field of black hole and all the light like paths will warp so as to fall farther to the hole. Before arriving to the Schwarzschild’s Sphere, object faces with length extension because of the difference between amount of tidal forces on the nearest and furthest points of object that take the object apart and after passing the Schwarzschild’s sphere, based on the Special relativity of Einstein, the parts of object face with length contraction. In comparison between strange stars and black holes we conclude that core of strange stars has a temperature and pressure not sufficient for up and down quarks and they turn into strange ones. However, in core of black holes, because of massive stars and hot gases falling into it, they are always in a high temperature and pressure. So they can be made up of up and down quarks. At the Ergo sphere Region of black hole, a particle that gets into it will divide into 2 pieces, one of them falls into the black hole and another gets out of the Schwarzschild sphere very fast and it’s called the black hole radiation. According to the Diagram drawn by R. Rafini and J. Weeler, an object gets out of white hole in past space-time, it can be able to send signals to us and we can receive it but black hole which is located in future space-time, after object enters to the Schwarzschild’s Sphere, the signals it sends won’t be received. In order to reach the third space-time which is like a mirror to our universe, our speed needs to exceed the speed of light to pass the Einstein-Rosen Bridge. As a conclusion, structure of black holes can be made up of up and down quarks and everything falls into the black hole, collapses and turns into a bunch of quarks. Space-time around black holes, based on Rafini-Weeler diagram, is展开更多
In this paper, we consider Osserman conditions on lightlike warped product (sub-)manifolds with respect to the Jacobi Operator. We define the Jacobi operator for lightlike warped product manifold and introduce a study...In this paper, we consider Osserman conditions on lightlike warped product (sub-)manifolds with respect to the Jacobi Operator. We define the Jacobi operator for lightlike warped product manifold and introduce a study of lightlike warped product Osserman manifolds. For the coisotropic case with totally degenerates first factor, we prove that this class consists of Einstein and locally Osserman lightlike warped product.展开更多
基金supported by Beijing Natural Science Foundation(Grant No.1182006)National Natural Science Foundation of China(Grant No.11771020)。
文摘One of the fundamental problems in Finsler geometry is to study Finsler metrics of constant(or scalar)curvature.In this paper,we refine and improve Chen-Shen-Zhao equations characterizing Finsler warped product metrics of scalar flag curvature.In particular,we find equations that characterize Finsler warped product metrics of constant flag curvature.Then we improve the Chen-Shen-Zhao result on characterizing Einstein Finsler warped product metrics.As its application we construct explicitly many new warped product Douglas metrics of constant Ricci curvature by using known locally projectively flat spherically symmetric metrics of constant flag curvature.
基金Natural Science Foundation of Xinjiang Uygur Autonomous Region,China(Grant No.2015211C277)。
文摘Doubly warped product of Finsler manifolds is useful in theoretical physics,particularly in general relativity.In this paper,we study doubly warped product of Finsler manifolds with isotropic mean Berwald curvature or weak isotropic S-curvature.
基金supported by Program for New Century Excellent Talents in University(NCET-13-0510)National Natural Science Foundation of China(11271304,11571288,11461064)+1 种基金the Fujian Province Natural Science Funds for Distinguished Young Scholar(2013J06001)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry
文摘Let （M1, F1） and （M2, F2） be two strongly pseudoconvex complex Finsler man- ifolds. The doubly wraped product complex Finsler manifold （f2 M1 x h M2, F） of （M1, F1） and （M2, F2） is the product manifold M1 x M2 endowed with the warped product complex 2 2 Finsler metric F2 = f2F1 ＋ fl F2, where fl and f2 are positive smooth functions on M1 and M2, respectively. In this paper, the most often used complex Finsler connections, holomorphic curvature, Ricci scalar curvature, and real geodesics of the DWP-complex Finsler manifold are derived in terms of the corresponding objects of its components. Necessary and sufficient conditions for the DWP-complex Finsler manifold to be K/ihler Finsler （resp., weakly K/ihler Finsler, complex Berwald, weakly complex Berwald, complex Landsberg） manifold are ob- tained, respectively. It is proved that if （M1, F1） and （M2,F2） are projectively flat, then the DWP-complex Finsler manifold is projectively flat if and only if fl and f2 are positive constants.
文摘Based on the Mach’s principle, black holes warp the space time in a way that geodesic for every object which is moving toward black hole starts to bend and object starts to rotate around the black hole. Even light cannot be able to escape from the strong gravitational field of black hole and all the light like paths will warp so as to fall farther to the hole. Before arriving to the Schwarzschild’s Sphere, object faces with length extension because of the difference between amount of tidal forces on the nearest and furthest points of object that take the object apart and after passing the Schwarzschild’s sphere, based on the Special relativity of Einstein, the parts of object face with length contraction. In comparison between strange stars and black holes we conclude that core of strange stars has a temperature and pressure not sufficient for up and down quarks and they turn into strange ones. However, in core of black holes, because of massive stars and hot gases falling into it, they are always in a high temperature and pressure. So they can be made up of up and down quarks. At the Ergo sphere Region of black hole, a particle that gets into it will divide into 2 pieces, one of them falls into the black hole and another gets out of the Schwarzschild sphere very fast and it’s called the black hole radiation. According to the Diagram drawn by R. Rafini and J. Weeler, an object gets out of white hole in past space-time, it can be able to send signals to us and we can receive it but black hole which is located in future space-time, after object enters to the Schwarzschild’s Sphere, the signals it sends won’t be received. In order to reach the third space-time which is like a mirror to our universe, our speed needs to exceed the speed of light to pass the Einstein-Rosen Bridge. As a conclusion, structure of black holes can be made up of up and down quarks and everything falls into the black hole, collapses and turns into a bunch of quarks. Space-time around black holes, based on Rafini-Weeler diagram, is
文摘In this paper, we consider Osserman conditions on lightlike warped product (sub-)manifolds with respect to the Jacobi Operator. We define the Jacobi operator for lightlike warped product manifold and introduce a study of lightlike warped product Osserman manifolds. For the coisotropic case with totally degenerates first factor, we prove that this class consists of Einstein and locally Osserman lightlike warped product.
