共查询到10条相似文献,搜索用时 46 毫秒
1.
In this paper, we obtain a constraint of the mean curvature for proper biharmonic submanifolds in a sphere. We give some characterizations
of some proper biharmonic submanifolds with parallel mean curvature vector in a sphere. We also construct some new examples
of proper biharmonic submanifolds in a sphere. 相似文献
2.
We present some results on the boundedness of the mean curvature of proper biharmonic submanifolds in spheres. A partial classification result for proper biharmonic submanifolds with parallel mean curvature vector field in spheres is obtained. Then, we completely classify the proper biharmonic submanifolds in spheres with parallel mean curvature vector field and parallel Weingarten operator associated to the mean curvature vector field. 相似文献
3.
We study biharmonic submanifolds in δ-pinched Riemannian manifolds, and obtain some sufficient conditions for biharmonic submanifolds to be minimal ones. 相似文献
4.
Classification results for biharmonic submanifolds in spheres 总被引:1,自引:0,他引:1
We study biharmonic submanifolds of the Euclidean sphere that satisfy certain geometric properties. We classify: (i) the biharmonic
hypersurfaces with at most two distinct principal curvatures; (ii) the conformally flat biharmonic hypersurfaces. We obtain
some rigidity results for pseudoumbilical biharmonic submanifolds of codimension 2 and for biharmonic surfaces with parallel
mean curvature vector field. We also study the type, in the sense of B-Y. Chen, of compact proper biharmonic submanifolds
with constant mean curvature in spheres.
Dedicated to Professor Vasile Oproiu on his 65th birthday
The first author was supported by a INdAM doctoral fellowship, Italy.
The second author was supported by PRIN 2005, Italy.
The third author was supported by Grant CEEX ET 5871/2006, Romania 相似文献
5.
Julien Roth 《Journal of Geometry》2013,104(2):375-381
We investigate biharmonic submanifolds of the product of two space forms. We prove a necessary and sufficient condition for biharmonic submanifolds in these product spaces. Then, we obtain mean curvature estimates for proper-biharmonic submanifold of a product of two unit spheres. We also prove a non-existence result in the case of the product of a sphere and a hyperbolic space. 相似文献
6.
7.
Bang-Yen Chen 《Israel Journal of Mathematics》1995,91(1-3):373-391
In [3] the author initiated the study of submanifolds whose mean curvature vectorH is an eigenvector of the Laplacian Δ and proved that such submanifolds are either biharmonic or of 1-type or of null 2-type.
The classification of surfaces with ΔH=λH in a Euclidean 3-space was done by the author in 1988. Moreover, in [4] the author classified such submanifolds in hyperbolic
spaces. In this article we study this problem for space-like submanifolds of the Minkowski space-timeE
1
m
when the submanifolds lie in a de Sitter space-time. As a result, we characterize and classify such submanifolds in de Sitter
space-times. 相似文献
8.
We obtain several rigidity results for biharmonic submanifolds in $\mathbb{S}^{n}$ with parallel normalized mean curvature vector fields. We classify biharmonic submanifolds in $\mathbb{S}^{n}$ with parallel normalized mean curvature vector fields and with at most two distinct principal curvatures. In particular, we determine all biharmonic surfaces with parallel normalized mean curvature vector fields in $\mathbb{S}^{n}$ . Then we investigate, for (not necessarily compact) proper-biharmonic submanifolds in $\mathbb{S}^{n}$ , their type in the sense of B.-Y. Chen. We prove that (i) a proper-biharmonic submanifold in $\mathbb{S}^{n}$ is of 1-type or 2-type if and only if it has constant mean curvature f=1 or f∈(0,1), respectively; and (ii) there are no proper-biharmonic 3-type submanifolds with parallel normalized mean curvature vector fields in $\mathbb{S}^{n}$ . 相似文献
9.
An important theorem about biharmonic submanifolds proved independently by Chen-Ishikawa (Kyushu J Math 52(1):167?C185, 1998) and Jiang (Chin Ann Math Ser. 8A:376?C383, 1987) states that an isometric immersion of a surface into 3-dimensional Euclidean space is biharmonic if and only if it is harmonic (i.e, minimal). In a later paper, Caddeo et?al. (Isr J Math 130:109?C123, 2002) showed that the theorem remains true if the target Euclidean space is replaced by a 3-dimensional hyperbolic space form. In this paper, we prove the dual results for Riemannian submersions, i.e., a Riemannian submersion from a 3-dimensional space form into a surface is biharmonic if and only if it is harmonic. 相似文献
10.
We consider a complete biharmonic immersed submanifold M in a Euclidean space ${\mathbb{E}^N}$ . Assume that the immersion is proper, that is, the preimage of every compact set in ${\mathbb{E}^N}$ is also compact in M. Then, we prove that M is minimal. It is considered as an affirmative answer to the global version of Chen’s conjecture for biharmonic submanifolds. 相似文献