相关论文: On Pseudo-Umbilical Spacelike Submanifolds in Inde…
A totally umbilical submanifold in pseudo-Riemannian manifolds is a fundamental notion, which is characterized by the condition that the second fundamental form is proportional to the metric. It is also a generalization of the notion of a…
The purpose of this paper is to classify totally umbilical slant submanifolds of a Kenmotsu manifold. We prove that a totally umbilical slant submanifold $M$ of a Kenmotsu manifold $\bar M$ is either invariant or anti-invariant or $dim M=1$…
Given a semi-Riemannian manifold, we give necessary and sufficient conditions for a Riemannian submanifold of arbitrary co-dimension to be umbilical along normal directions. We do that by using the so-called \emph{total shear tensor}, i.e.,…
The object of this paper is to study the invariant submanifolds of Sasakian generalized-Sasakian-space-form. Here, we obtain some equivalent conditions for an invariant submanifold of a Sasakian generalized-Sasakian-space-forms to be…
In this article we study isometric immersions of nearly K\"ahler manifolds into a space form (specially Euclidean space) and show that every nearly K\"ahler submanifold of a space form has a totally umbilic foliation whose leafs are…
We classify maximal totally geodesic submanifolds in exceptional symmetric spaces up to isometry. Moreover, we introduce an invariant for certain totally geodesic embeddings of semisimple symmetric spaces, which we call the Dynkin index. We…
We present classifications of totally geodesic and totally umbilical Legendrian submanifolds of $(\kappa,\mu)$-spaces with Boeckx invariant $I \leq -1$. In particular, we prove that such submanifolds must be, up to local isometries, among…
We show that a totally geodesic submanifold of a symmetric space satisfying certain conditions admits an extension to a minimal submanifold of dimension one higher, and we apply this result to construct new examples of complete embedded…
Compared to totally umbilical submanifolds, studies on pseudo-umbilical submanifolds are quite limited. In this paper, pseudo-umbilical submanifolds of locally product Riemannian manifolds are studied. Necessary and sufficient conditions…
We prove some Bernstein theorems for entire space-like submanifolds in pseudo-Euclidean spaces and, as a corollary, we obtain a new proof of the Calabi-Pogorelov theorem on global solutions of Monge-Ampere equations.
In this paper we establish conditions on the length of the traceless part of the second fundamental form of a complete constant mean curvature hypersurface immersed in a space of constant sectional curvature in order to show that it is…
We introduce the class of almost symmetric submanifolds of Euclidean space, a close relative of symmetric submanifolds and (contact) sub-Riemannian symmetric spaces. More specifically, we prove that every full irreducible almost symmetric…
In this work, we study the geometric properties of spacelike foliations by hypersurfaces on a Lorentz manifold. We investigate conditions for the leaves being stable, totally geodesic or totally umbilical. We consider that…
Let M be a compact pseudo-umbilical submanifold of the unit sphere S. In the present note, it is shown that if the normal curvature, scalar curvature S and square of the length of second fundamental form satisfy certain conditions, then M…
We introduce semi-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion and find…
We prove that equivariant, holomorphic embeddings of Hermitian symmetric spaces are totally geodesic (when the image is not of exceptional type).
In this article we classify totally geodesic submanifolds in arbitrary products of rank one symmetric spaces. Furthermore, we give infinitely many examples of irreducible totally geodesic submanifolds in Hermitian symmetric spaces with…
It is proved, that if M is a connected, complete submanifold of a complex space form N and each geodesic of M lies in an 1-dimensional totally geodesic complex submanifold of N, then M is totally geodesic in N and is a real space form or a…
We completely describe inhomogeneous properly embedded almost symmetric submanifolds of Euclidean space as certain unions of parallel symmetric submanifolds of the ambient Euclidean space.
We prove an isoperimetric-type inequality for maximal, spacelike submanifold in the Minkowski space. The argument is based on the recent work of Brendle.