In this paper,we consider quasi Einstein hypersurfaces in a hyperbolic space. The following theorem is obtained. Theorem Quasi Einstein hypersurfaces of a hyperbolic space are of constant curvature,where the dimension...In this paper,we consider quasi Einstein hypersurfaces in a hyperbolic space. The following theorem is obtained. Theorem Quasi Einstein hypersurfaces of a hyperbolic space are of constant curvature,where the dimension is large enough.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
In this paper, we find some new homogeneous manifolds G/H admitting non-Riemannian EinsteinRanders metrics when G is the compact simple Lie group E6, or E7 or E8. In the beginning, we prove that these homogeneous mani...In this paper, we find some new homogeneous manifolds G/H admitting non-Riemannian EinsteinRanders metrics when G is the compact simple Lie group E6, or E7 or E8. In the beginning, we prove that these homogeneous manifolds admit Riemannian Einstein metrics. Based on these metrics, we obtain non-Riemannian Einstein Randers metrics on them.展开更多
We use a Killing form on a Riemannian manifold to construct a class of Finsler metrics. We find equations that characterize Einstein metrics among this class. In particular, we construct a family of Einstein metrics o...We use a Killing form on a Riemannian manifold to construct a class of Finsler metrics. We find equations that characterize Einstein metrics among this class. In particular, we construct a family of Einstein metrics on S^3 with Ric = 2F^2, Ric = 0 and Ric =-2F^2, respectively. This family of metrics provides an important class of Finsler metrics in dimension three, whose Ricci curvature is a constant, but the flag curvature is not.展开更多
Let N be a compact complex submanifold of a compact complex manifold M. We say that Nsplits in M, if the holomorphic tangent bundle sequence splits holomorphically. By a result of Mok, a splittingsubmanifold of a Khle...Let N be a compact complex submanifold of a compact complex manifold M. We say that Nsplits in M, if the holomorphic tangent bundle sequence splits holomorphically. By a result of Mok, a splittingsubmanifold of a Khler-Einstein manifold with a projective structure is totally geodesic. The classification ofall splitting submanifolds of families of fake elliptic curves given here completes the case of threefolds M with aprojective structure by a previous result of the authors.展开更多
文摘In this paper,we consider quasi Einstein hypersurfaces in a hyperbolic space. The following theorem is obtained. Theorem Quasi Einstein hypersurfaces of a hyperbolic space are of constant curvature,where the dimension is large enough.
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 National Natural Science Foundation of China(Grant Nos.10971104,11001133 and 11221091)
文摘In this paper, we find some new homogeneous manifolds G/H admitting non-Riemannian EinsteinRanders metrics when G is the compact simple Lie group E6, or E7 or E8. In the beginning, we prove that these homogeneous manifolds admit Riemannian Einstein metrics. Based on these metrics, we obtain non-Riemannian Einstein Randers metrics on them.
基金supported by National Natural Science Foundation of China (Grant No. 11371386)the European Union’s Seventh Framework Programme (FP7/2007–2013) (Grant No. 317721)National Science Foundation of USA (Grant No. DMS-0810159)
文摘We use a Killing form on a Riemannian manifold to construct a class of Finsler metrics. We find equations that characterize Einstein metrics among this class. In particular, we construct a family of Einstein metrics on S^3 with Ric = 2F^2, Ric = 0 and Ric =-2F^2, respectively. This family of metrics provides an important class of Finsler metrics in dimension three, whose Ricci curvature is a constant, but the flag curvature is not.
文摘Let N be a compact complex submanifold of a compact complex manifold M. We say that Nsplits in M, if the holomorphic tangent bundle sequence splits holomorphically. By a result of Mok, a splittingsubmanifold of a Khler-Einstein manifold with a projective structure is totally geodesic. The classification ofall splitting submanifolds of families of fake elliptic curves given here completes the case of threefolds M with aprojective structure by a previous result of the authors.
