共查询到20条相似文献,搜索用时 15 毫秒
1.
We study pseudosymmetric lightlike hypersurfaces of an indefinite Sasakian space form, tangent to the structure vector field. We obtain sufficient conditions for a lightlike hypersurface to be pseudosymmetric, pseudoparallel and Ricci-pseudosymmetric in an indefinite Sasakian space form. We also find certain conditions for a pseudosymmetric lightlike hypersurface of an indefinite Sasakian space form to be totally geodesic and check the effect of Weyl projective pseudosymmetry conditions on the geometry of a lightlike hypersurface of an indefinite Sasakian space form. Moreover we give some physical interpretations of pseudo-symmetry conditions. 相似文献
2.
In this article, after giving a necessary and sufficient condition for two Einstein- Weyl manifolds to be in conformal correspondence, we prove that any conformal mapping between such manifolds is generalized concircular if and only if the covector field of the conformal mapping is locally a gradient. Using this fact we deduce that any conformal mapping between two isotropic Weyl manifolds is a generalized concircular mapping. Moreover, it is shown that a generalized concircularly flat Weyl manifold is generalized concircular to an Einstein manifold and that its scalar curvature is prolonged covariant constant. 相似文献
3.
In this article, after giving a necessary and sufficient condition for two Einstein-Weyl manifolds to be in conformal correspondence, we prove that any conformal mapping between such manifolds is generalized concircular if and only if the covector field of the conformal mapping is locally a gradient. Using this fact we deduce that any conformal mapping between two isotropic Weyl manifolds is a generalized concircular mapping. Moreover, it is shown that a generalized concircularly flat Weyl manifold is generalized concircular to an Einstein manifold and that its scalar curvature is prolonged covariant constant. 相似文献
4.
The theory of Ribaucour transformations for hypersurfaces in space forms is established. For any such hypersurface M, that admits orthonormal principal vector fields, it was shown the existence of a totally umbilic hypersurface locally associated to M by a Ribaucour transformation. A method of obtaining linear Weingarten surfaces in a three-dimensional space form is provided. By applying the theory, a new one-parameter family of complete constant mean curvature (cmc) surfaces in the unit sphere, locally associated to the flat torus, is obtained. The family contains a class of complete cmc cylinders in the sphere. In particular, one gets a family of complete minimal surfaces and minimal cylinders, locally associated to the Clifford torus.Mathematics Subject Classifications (2000): 53C20. 相似文献
5.
The main result of this paper states that any 2-quasi-umbilical hypersurface of a semi-Riemannian conformally flat space is a manifold with pseudosymmetric Weyl tensor. 相似文献
6.
In this paper we study the topological and metric rigidity of hypersurfaces in ℍ
n+1, the (n + 1)-dimensional hyperbolic space of sectional curvature −1. We find conditions to ensure a complete connected oriented hypersurface
in ℍ
n+1 to be diffeomorphic to a Euclidean sphere. We also give sufficient conditions for a complete connected oriented closed hypersurface
with constant norm of the second fundamental form to be totally umbilic. 相似文献
7.
YONGFAN Zheng 《Geometriae Dedicata》1997,67(3):295-300
Let M be a compact orientable submanifold immersed in a Riemannian manifold of constant curvature with flat normal bundle. This paper gives intrinsic conditions for M to be totally umbilical or a local product of several totally umbilical submanifolds. It is proved especially that a compact hypersurface in the Euclidean space with constant scalar curvature and nonnegative Ricci curvature is a sphere. 相似文献
8.
Sharief Deshmukh 《Monatshefte für Mathematik》2014,174(3):413-426
We study the influence of a unit Killing vector field on the geometry of a hypersurface in the unit sphere. The combination of the Killing vector field on the hypersurface and the conformal vector field on the ambient sphere triggers the presence of four specific smooth functions on the hypersurface, we use these four functions to derive different sufficient conditions for a hypersurface to be the totally geodesic sphere and for a minimal hypersurface to be the totally geodesic sphere, Clifford minimal hypersurface respectively. In particular we classify compact minimal hypersurfaces with a unit Killing vector field in the unit sphere. 相似文献
9.
10.
Relationships between the orthogonal direct sum decomposition of a vector space over a finite field and the existence of the generalized inverses of a linear transformation over the finite field are analyzed. Necessary and sufficient conditions for judging the existence of the generalized inverses of a linear transformation over a finite field are presented. 相似文献
11.
Peter Kohlmann 《Journal of Geometric Analysis》2001,11(2):295-310
We establish very general Weyl identities for pairs of symmetric functions of the invariants of the shape operator of a hypersurface
in a space form or a general Codazzi tensor, respectively. They are used to characterize certain isoparametric hypersurfaces
by assuming constancy or extremal properties of the functions, provided they fulfill ellipticity and/or convexity (concavity)
properties. This way, many wellknown results are generalized. Finally, a chain rule for Weyl identities offers additional
extension of some results. 相似文献
12.
In this paper, we study the relations between a compact spacelike hypersurface with hy-perplanar boundary in the (n 1)- dimensional Minkowski space-time L^n 1 being totally umbilicaland its hyperplanar boundary in a fixed hyperplane π of L^(n 1) being totally umbilical under certainconditions. We give the sufficient conditions for such hypersurface and its hyperplanar boundary tobe totally umbilical in their respective ambients. 相似文献
13.
METRIC GENERALIZED INVERSE OF LINEAR OPERATOR IN BANACH SPACE*** 总被引:13,自引:0,他引:13
The Moore-Penrose metric generalized inverse T of linear operator T in Banach space is systematically investigated in this paper. Unlike the case in Hilbert space, even T is a linear operator in Banach Space, the Moore-Penrose metric generalized inverse T is usually homogeneous and nonlinear in general. By means of the methods of geometry of Banach Space, the necessary and sufficient conditions for existence, continuitv, linearity and minimum property of the Moore-Penrose metric generalized inverse T will be given, and some properties of T will be investigated in this paper. 相似文献
14.
Jong Ryul Kim 《Comptes Rendus Mathematique》2013,351(11-12):471-475
For an extrinsic symmetric space M in Minkowski space-time, we prove that if M is spacelike with zero mean curvature, then it is totally geodesic and if M is timelike with zero mean curvature, then it is totally geodesic or it is a flat hypersurface. 相似文献
15.
《Optimization》2012,61(6):763-780
The notion of covering is introduced for a set-valued mapping defined on an arbitrary set in a Banach space. A necessary and sufficient covering criterion is proved. The conditions are formulated in terms of generalized differentials and generalized normals. The covering theorem is applied to deduce formulas of generalized differential calculus and necessary optimality conditions for nonsroooth optimization problems. 相似文献
16.
Let f : M^n→S^n 1真包含于R^n 2 be an n-dimensional complete oriented Riemannian manifold minimally immersed in an (n 1)-dimensional unit sphere S^n 1. Denote by S^n 1 the upper closed hemisphere. If f(M^n)包含于S ^n 1, then under some curvature conditions the authors can get that the isometric immersion is a totally embedding. They also generalize a theorem of Li Hai Zhong on hypersurface of space form with costant scalar curvature. 相似文献
17.
Theodoros Vlachos 《Geometriae Dedicata》1997,68(1):73-78
We use the maximum principle for second-order elliptic operators to establish a sufficient condition for a compact hypersurface in a space form to be a geodesic sphere in terms of a pinching for the s-mean curvature. 相似文献
18.
Shen yibing 《数学年刊B辑(英文版)》1984,5(4):625-632
This paper gives some sufficient conditions for a compact submanifold with nonnegative sectional curvature in a space form to be totally umbilical. In particular, for a compact submanifold M with flat normal bundle, if the scalar curvature is proportional to the mean curvature everywhere, then M is totally umbilical or the Riemannian product of several totally umbilical constantly curved submanifolds. 相似文献
19.
对于Banach空间中余一维闭值域有界线性算子的集值度量广义逆,给出其具有连续线性选择的充分必要条件.结果是对M.Z.Nashed与G.F.Votruba提出的研究问题的部分回答. 相似文献