In this paper, we prove the following two main results: i) Let M be a mixed foliate non-trivial CR Submanifold of a Sasakian space form M(c). If the (D,⊥D) is ξ-horizontal, then c≤1. ii) Let M be a mixed faliate ge...In this paper, we prove the following two main results: i) Let M be a mixed foliate non-trivial CR Submanifold of a Sasakian space form M(c). If the (D,⊥D) is ξ-horizontal, then c≤1. ii) Let M be a mixed faliate generic Submanifold of a Sasakian Space form M^(2m)+1(c). If the(D,⊥) is ξ-horizontal and the f-structure P oa M is paralIel, then M is an (m+l)-dimensional anti-invariant Submanifold of M^(2m+1(c) or, c=1.展开更多
t The authors consider the problem of conformally deforming a metric such that the k-curvature defined by an elementary symmetric function of the eigenvalues of the Bakry-Emery Ricci tensor on a compact manifold with ...t The authors consider the problem of conformally deforming a metric such that the k-curvature defined by an elementary symmetric function of the eigenvalues of the Bakry-Emery Ricci tensor on a compact manifold with boundary to a prescribed function. A consequence of our main result is that there exists a complete metric such that the Monge-Amp^re type equation with respect to its Bakry-Emery Ricci tensor is solvable, provided that the initial Bakry-Emery Ricci tensor belongs to a negative convex cone.展开更多
文摘In this paper, we prove the following two main results: i) Let M be a mixed foliate non-trivial CR Submanifold of a Sasakian space form M(c). If the (D,⊥D) is ξ-horizontal, then c≤1. ii) Let M be a mixed faliate generic Submanifold of a Sasakian Space form M^(2m)+1(c). If the(D,⊥) is ξ-horizontal and the f-structure P oa M is paralIel, then M is an (m+l)-dimensional anti-invariant Submanifold of M^(2m+1(c) or, c=1.
基金Project supported by the National Natural Science Foundation of China(Nos.10831008,11131007)
文摘t The authors consider the problem of conformally deforming a metric such that the k-curvature defined by an elementary symmetric function of the eigenvalues of the Bakry-Emery Ricci tensor on a compact manifold with boundary to a prescribed function. A consequence of our main result is that there exists a complete metric such that the Monge-Amp^re type equation with respect to its Bakry-Emery Ricci tensor is solvable, provided that the initial Bakry-Emery Ricci tensor belongs to a negative convex cone.
