共查询到17条相似文献,搜索用时 34 毫秒
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我们给出了欧氏椭球面$Q^{n+1}(c,d)$中平行超曲面的完全分类,并且证明了$Q^{n+1}(c,d)$中的超曲面是全脐的当且仅当它是平行的. 相似文献
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<正> 最近,胡和生证明了如下的命题:如果黎曼空间 V_(n+1)容有三系相互直交的常曲率全测地超曲面,那末 V_(n+1)是常曲率的,而且这些超曲面的曲率都相等.本文的目的是把这里全测地的条件换成较广泛的全脐点条件而证明同一结果.设 V_(+1)的基本张量是 α_(αβ)(α,β=1,…,n+1),而且超曲面V_n~((1))的方程是 相似文献
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Let Vn be Riemannian space of genernal constant curvature.In this paper, we have proved following;Theorem I If a Vn(n≥5 ) admits three mutually orthogonal families oftotally numbilical hypersurfaces such that they are of constant curvature and Einsteinian and of general constant curvature respectively, then Vn is space with constant curvature.Theorem 2 If a Vn ( n ≥ 5 ) admits three mutually orthogonal famities of totally umbilical hypersurfaces, of which one is conformally flat and other two are Einsteinian and of constant curvature respectively, and latter either is of constant meam curvature, then Vn is of constant curvature. 相似文献
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1.引言在[1]中,Calabi证明了n+1(n≤4)维Minkowski空间中的完备极大类空超曲面是全测地的。在[2]中 , Cheng-Yau对所有的n证明了这一结论。在[3]中,对于某一类Lorentz流形,Nishikawa证明了类似的结果。并且在[2]中,Cheng-Yau还证明了当具有常数平均曲率的类空超曲面M是Minkowski空间的闭子集时,有 相似文献
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The main result obtaind in this paper is that :Let M be a totally umbilical submanifolds in Riemannian manifold N. If the Weyl conformal curvature tensor for N satisfies the following condition: ▽xC=ω(X)C, for some 1-form ω and any vector field X in M, then M is con-formally flat or it is totally geodesic . 相似文献
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In this paper we obtain some formulas for totally umbilical hypersurfaces in a locally symmetric manifold, and derive some local results on the hypersurfaces from these formulas. 相似文献
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In Perez (Thesis, 2011), Perez proved some L 2 inequalities for closed convex hypersurfaces immersed in the Euclidean space ? n+1, and more generally for closed hypersurfaces with non-negative Ricci curvature, immersed in an Einstein manifold. In this paper, we discuss the rigidity of these inequalities when the ambient manifold is ? n+1, the hyperbolic space ? n+1, or the closed hemisphere \(\mathbb{S}_{+}^{n+1}\) . We also obtain a generalization of Perez’s theorem to the hypersurfaces without the hypothesis of non-negative Ricci curvature. 相似文献
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Rafael O. Ruggiero 《Geometriae Dedicata》1999,78(2):161-170
We show that complete, simply connected Riemannian manifolds admitting continuous foliations by geodesics with integrable orthogonal distributions are homeomorphic to products F×R. Moreover, the geodesics in the foliation are global minimizers. 相似文献
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We consider almost contact metric hypersurfaces of almost Hermitian manifolds of class W3 (in the Gray–Hervella terminology). We establish a criterion for minimality of such hypersurfaces in the case when the contact metric structure is cosymplectic. 相似文献
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Eleutherius Symeonidis 《Complex Analysis and Operator Theory》2017,11(8):1747-1763
We establish a general concept of families of hypersurfaces over which the integral of a harmonic function remains invariant. Passing to the limit these hypersurfaces often degenerate, a fact that renders the majority of the classical mean value properties, and also helps to find new ones. 相似文献
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Real hypersurfaces of a complex manifold admit a naturally induced almost contact structure F′ from the almost complex structure of the ambient manifold. We prove that for any F′-invariant submanifold M of a geodesic hypersphere in a non-flat complex space form and of a horosphere in a complex hyperbolic space, its second fundamental form h satisfies the condition h(FX,Y ) - h(X, FY) = g(FX, Y )h, X,Y ? T(M), 0 1 h ? T^(M){h(FX,Y ) - h(X, FY) = g(FX, Y )eta, X,Y in T(M), 0 ne eta in {T^perp}(M)}, which has been considered in [2] and [3]. 相似文献