共查询到20条相似文献,搜索用时 15 毫秒
1.
Luis Guijarro 《Proceedings of the American Mathematical Society》1998,126(5):1541-1545
The soul theorem states that any open Riemannian manifold with nonnegative sectional curvature contains a totally geodesic compact submanifold such that is diffeomorphic to the normal bundle of . In this paper we show how to modify into a new metric so that:
- has nonnegative sectional curvature and soul .
- The normal exponential map of is a diffeomorphism.
- splits as a product outside of a compact set.
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Yu. G. Nikonorov 《Siberian Advances in Mathematics》2014,24(3):187-192
We find a convenient expression for the value of the covariant curvature 4-tensor of an arbitrary Riemannian manifold on a quadruple of its Killing vector fields. With its use, we in particular obtain a simple deduction of the well-known formula to calculate the sectional curvature of a homogeneous Riemannian space. 相似文献
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Ramesh Sharma 《Journal of Geometry》1995,53(1-2):179-190
Some results on Ricci-symmetric contact metric manifolds are obtained. Second order parallel tensors and vector fields keeping curvature tensor invariant are characterized on a class of contact manifolds. Conformally flat contact manifolds are studied assuming certain curvature conditions. Finally some results onk-nullity distribution of contact manifolds are obtained. 相似文献
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We have studied the normality of an almost contact metric hypersurface of a Kahler manifold. Quasi-umbilical and umbilical properties have also been studied. 相似文献
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Luigia Di Terlizzi 《Acta Mathematica Hungarica》2006,110(3):225-239
Summary We consider a genaralization of contact metric manifolds given by assignment of 1-formsη1, . . . ,ηsand a compatible metric gon a manifold. With some integrability conditions they are called almost<span style='font-size:10.0pt;font-family:"Monotype
Corsiva"; mso-bidi-font-family:"Monotype Corsiva"'>S-manifolds. We give a sufficient condition regarding the curvature of
an almost<span style='font-size:10.0pt;font-family:"Monotype Corsiva";mso-bidi-font-family: "Monotype Corsiva"'>S-manifold
to be locally isometric to a product of a Euclidean space and a sphere. 相似文献
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Gerd Kainz 《Monatshefte für Mathematik》1984,98(3):211-217
E. Binz [1] considered two canonical Riemannian metrics on the space of embeddings of a closed (n–1) dimensional manifold into
n
, and computed the geodesic sprays. Here we consider the space of immersions Imm (M, N) whereM is without boundary, and we compute the covariant derivative (in the form of its connector) and the Riemannian curvature of one of these metrics, the non trivial one. The setting is close to that used byP. Michor [2], and we refer the reader to this paper for notation. 相似文献
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We investigate the traceless component of the conformal curvature tensor defined by (2.1) in Kähler manifolds of dimension ? 4, and show that the traceless component is invariant under concircular change. In particular, we determine Kähler manifolds with vanishing traceless component and improve some theorems (for example, [4, pp. 313–317]) concerning the conformal curvature tensor and the spectrum of the Laplacian acting on p (0 ? p ? 2)-forms on the manifold by using the traceless component. 相似文献
11.
Mileva Prvanovi? 《Journal of Geometry》2012,103(1):89-101
We consider an almost Hermitian manifold and apply the conformal change of metric to its holomorphic curvature tensor. In such a way we find that the generalized Bochner curvature tensor can be expressed as a linear combination of B 1, B 2, and B 3 such that (6.4) holds. Each of the tensors B 1, B 2, B 3 is conformally invariant and satisfies the condition (1.2) of K?hler type. 相似文献
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Seiichi Yamaguchi Hiroaki Nemoto Jae -Bok Jun 《Annali di Matematica Pura ed Applicata》1987,147(1):105-116
Summary The metric compound structure of rank r is an obstructed structure of an induced structure on a real submanifold in an almost Hermitian manifold. In this paper we deal with a submanifold with metric compound structure of rank 2 in a Kaehlerian manifold and we classify it under some suitable conditions. Namely it is a standard sphere or neither Einstein nor conformally flat. 相似文献
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T. Tshikuna-Matamba 《Periodica Mathematica Hungarica》2006,52(1):101-119
Summary In this paper, we discuss some geometric properties of three types of Riemannian submersions whose total space is an almost
contact metric manifold with 3-structure. The study is focused on the transference of structures. 相似文献
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We give geometric interpretations of a torsion tensor and curvature tensors in a generalized Finsler space (with an asymmetric basic tensor). 相似文献
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Geometriae Dedicata - 相似文献
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Osamu Kobayashi 《Mathematische Annalen》1987,279(2):253-265
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Let be a connected and simply-connected open subset of such that the geodesic distance in is equivalent to the Euclidean distance. Let there be given a Riemannian metric (gij) of class and of vanishing curvature in , such that the functions gij and their partial derivatives of order have continuous extensions to . Then there exists a connected open subset of containing and a Riemannian metric of class and of vanishing curvature in that extends the metric (gij). To cite this article: P.G. Ciarlet, C. Mardare, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献