共查询到20条相似文献,搜索用时 843 毫秒
1.
J. -H. Eschenburg 《manuscripta mathematica》1989,64(1):55-75
We give an intrinsic proof and a generalization of the interior and boundary maximum principle for hypersurfaces in Riemannian and Lorentzian manifolds. Moreover, we show some new applications to manifolds with lower Ricci curvature bounds. E.g. we prove a local and a Lorentzian version of Cheng's maximal diameter theorem and a non-existence result for closed minimal hypersurfaces. 相似文献
2.
《复变函数与椭圆型方程》2012,57(3):277-282
We give a simple proof of a Riemann mapping theorem for domains in a Stein manifold with a spherical boundary. Those boundaries are real hypersurfaces which are locally CR equivalent to the sphere inside complex space. The main observation is that for higher dimensional Stein manifolds, the fundamental group of its boundary coincides with that of its interior. 相似文献
3.
Bernd Wegner 《Journal of Geometry》1989,36(1-2):183-187
Transnormal manifolds are generalizations of convex hypersurfaces of constant width (see [7]). For such hypersurfaces it is known that every orthogonal projection onto a hyperplane has an outline which is of constant width, too. Orthogonal projections of transnormal manifolds have been studied by F.J. Craveiro de Carvalho [1] in the case when the projection is an immersion onto a convex hypersurface of constant width in a suitable affine subspace of the ambient Euclidean space.Here it will be shown that transnormality is not preserved under orthogonal projection onto hyperplanes without assuming that the manifold has the topological type of a sphere. This implies another general version of the transnormal graph theorem (see [2]). Furthermore, in the case of closed transnormal curves in 3-space also non-orthogonal parallel projection onto planes cannot preserve transnormality as is shown in the last section. 相似文献
4.
A. Caminha 《Bulletin of the Brazilian Mathematical Society》2011,42(2):277-300
In this paper we examine different aspects of the geometry of closed conformal vector fields on Riemannian manifolds. We begin
by getting obstructions to the existence of closed conformal and nonparallel vector fields on complete manifolds with nonpositive
Ricci curvature, thus generalizing a theorem of T.K. Pan. Then we explain why it is so difficult to find examples, other than
trivial ones, of spaces having at least two closed, conformal and homothetic vector fields. We then focus on isometric immersions,
firstly generalizing a theorem of J. Simons on cones with parallel mean curvature to spaces furnished with a closed, Ricci
null conformal vector field; then we prove general Bernstein-type theorems for certain complete, not necessarily cmc, hypersurfaces
of Riemannian manifolds furnished with closed conformal vector fields. In particular, we obtain a generalization of theorems
J. Jellett and A. Barros and P. Sousa for complete cmc radial graphs over finitely punctured geodesic spheres of Riemannian
space forms. 相似文献
5.
In this paper, we prove a one end theorem for complete noncompact Riemannian manifolds and apply it to complete noncompact
stable minimal hypersurfaces.
Received: 10 September 2007 相似文献
6.
Xu Cheng 《Geometriae Dedicata》2002,90(1):115-125
In this paper, we consider the coisotropic submanifolds in a Kähler manifold of nonnegative holomorphic curvature. We prove an intersection theorem for compact totally geodesic coisotropic submanifolds and discuss some topological obstructions for the existence of such submanifolds. Our results apply to Lagrangian submanifolds and real hypersurfaces since the class of coisotropic submanifolds includes them. As an application, we give a fixed-point theorem for compact Kähler manifolds with positive holomorphic curvature. Also, our results can be further extended to nearly Kähler manifolds. 相似文献
7.
Bang-Yen Chen 《Results in Mathematics》2005,48(1-2):9-26
The purpose of this article is the study of warped product manifolds which can be realized either as centroaffine or graph hypersurfaces in some affine space. First, we show that there exist many such realizations. Then we establish general optimal inequalities in terms of the warping function and the Tchebychev vector field for such affine hypersurfaces. We also investigate warped product affine hypersurfaces which verify the equality case of the inequalities. Several applications are also presented. 相似文献
8.
We study a class of submanifolds, called Generalized Cauchy-Riemann (GCR) lightlike submanifolds of indefinite Sasakian manifolds as an umbrella of invariant, screen real, contact CR lightlike subcases [8] and real hypersurfaces [9]. We prove existence and non-existence theorems and a characterization theorem on minimal GCR-lightlike submanifolds. 相似文献
9.
We introduce the notion of the lightcone Gauss–Kronecker curvature for a spacelike submanifold of codimension two in Minkowski
space, which is a generalization of the ordinary notion of Gauss curvature of hypersurfaces in Euclidean space. In the local
sense, this curvature describes the contact of such submanifolds with lightlike hyperplanes. We study geometric properties
of such curvatures and show a Gauss–Bonnet type theorem. As examples we have hypersurfaces in hyperbolic space, spacelike
hypersurfaces in the lightcone and spacelike hypersurfaces in de Sitter space. 相似文献
10.
Quasi—Einstein Hypersurfaces in a Hyperbolic Space 总被引:1,自引:0,他引:1
§1. IntroductionLetRijbethecomponentsofRiccitensorofann-dimensionalRiemannianmanifoldM.IfRij=Agij Bξiξj, (i,j=1,2,…,n)(1.1)whereξisanunitvectorfield,thenMiscalledaquasi-EinsteinmanifoldanddenotedbyQE(ξ).Ifξisanisotropicvectorfield,thenMiscalledageneralizedquasi-Einsteinmanifold.Intheequality(1.1),AandBarescalarfunctions.WeknowQE(ξ)manifoldisEinsteinwhenB≡0.Especially,if〈ξ,ξ〉=e=±1,thenQE(ξ)iscalledanormalquasi-Einsteinmani-fold.Itiseasytoknowfrom[1]and[2]:Rij=R-Tn-1… 相似文献
11.
We develop area and volume comparison theorems for the evolution of spacelike, acausal, causally complete hypersurfaces in Lorentzian manifolds, where one has a lower bound on the Ricci tensor along timelike curves, and an upper bound on the mean curvature of the hypersurface. Using these results, we give a new proof of Hawking’s singularity theorem. 相似文献
12.
In this article, we study isometric immersions of nearly Kähler manifolds into a space form (especially Euclidean space) and show that every nearly Kähler submanifold of a space form has an umbilic foliation whose leafs are 6-dimensional nearly Kähler manifolds. Moreover, using this foliation we show that there is no non-homogeneous 6-dimensional nearly Kähler submanifold of a space form. We prove some results towards a classification of nearly Kähler hypersurfaces in standard space forms. 相似文献
13.
本文证明了双曲空间中的共形平坦极小超曲面必为旋转超曲面或由一些旋转超曲面片用全测地超曲面片粘合而成.将这结果与王新民及许志才的一个已发表定理相组合,推广了Blair关于推广悬链面的一个定理. 相似文献
14.
Cícero P. Aquino 《Bulletin of the Brazilian Mathematical Society》2014,45(1):117-131
In this paper, we deal with complete hypersurfaces immersed in the hyperbolic space with constant scalar curvature. By supposing suitable restrictions on the Gauss mapping of such hypersurfaces we obtain some rigidity results. Our approach is based on the use of a generalized maximum principle, which can be seen as a sort of extension to complete (noncompact) Riemannian manifolds of the classical Hopf’s maximum principle. 相似文献
15.
Locally convex compact immersed hypersurfaces in the Finsler—Hadamard space with bounded T-curvature are considered. Under certain conditions on normal curvatures, such hypersurfaces are proved to be convex, embedded, and homeomorphic to the sphere. To this end, the Rauch theorem is generalized to exponential maps of hypersurfaces and the convexity of parallel hypersurfaces is proved. 相似文献
16.
By definition an orthogonal net on a pseudoriemannian manifold is a family of complementary foliations which intersect perpendicularly. There are derived generalizations of de Rham’s decomposition theorem by characterizing those pseudoriemannian manifolds equipped with an orthogonal net, which locally resp. globally allow a representation as a twisted resp. warped product. The results are applied for studying hypersurfaces with harmonic curvature. 相似文献
17.
Stefano Pigola 《Journal of Functional Analysis》2005,229(2):424-461
A general Liouville-type result and a corresponding vanishing theorem are proved under minimal regularity assumptions. The latter is then applied to conformal deformations of stable minimal hypersurfaces, to the L2 cohomology of complete manifolds, to harmonic maps under various geometric assumptions, and to the topology of submanifolds of Cartan-Hadamard spaces with controlled extrinsic geometry. 相似文献
18.
Christine Laurent-Thiébaut Jürgen Leiterer 《Annali di Matematica Pura ed Applicata》2001,180(1):59-70
Using Serre duality in CR manifolds and integral operators for the solution of the tangential Cauchy–Riemann equation with compact support, we prove
a separation theorem of Andreotti–Vesentini type for the -cohomology in q-concave real hypersurfaces.
Received: February 17, 1999?Published online: May 10, 2001 相似文献
19.
Galia Nakova 《Journal of Geometry》2013,104(3):539-556
In this paper we introduce radical transversal lightlike hypersurfaces of almost complex manifolds with Norden metric. Such class of lightlike hypersurfaces cannot exist for indefinite almost Hermitian manifolds. The considered lightlike hypersurfaces have two important properties. The first one is the uniqueness of their screen distributions, which implies that the induced geometric objects are well-defined. The second property is that the induced Ricci tensor on radical transversal lightlike hypersurface of a Kähler manifold with Norden metric is symmetric. This allows to define an induced scalar curvature of the hypersurface. We obtain new results about lightlike hypersurfaces concerning their relations with non-degenerate hypersurfaces of almost complex manifolds with Norden metric. Examples of the considered hypersurfaces are given. 相似文献
20.
This paper concerns the submanifold geometry in the ambient space of warped productmanifolds F^n×σ R, this is a large family of manifolds including the usual space forms R^m, S^m and H^m. We give the fundamental theorem for isometric immersions of hypersurfaces into warped product space R^n×σ R, which extends this kind of results from the space forms and several spaces recently considered by Daniel to the cases of infinitely many ambient spaces. 相似文献