Results 21 to 30 of about 67 (67)
Total mean curvatures of Riemannian hypersurfaces
Advanced Nonlinear Studies, 2023 We obtain a comparison formula for integrals of mean curvatures of Riemannian hypersurfaces via Reilly’s identities. As applications, we derive several geometric inequalities for a convex hypersurface Γ\Gamma in a Cartan-Hadamard manifold MM.
Ghomi Mohammad, Spruck Joel
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On hypersurfaces in a locally affine Riemannian Banach manifold II
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 2, Page 99-104, 2004., 2004 In our previous work (2002), we proved that an essential second‐order hypersurface in an infinite‐dimensional locally affine Riemannian Banach manifold is a Riemannian manifold of constant nonzero curvature. In this note, we prove the converse, in other words, we prove that a hypersurface of constant nonzero Riemannian curvature in a locally affine ...
El-Said R. Lashin, Tarek F. Mersal
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On the structure of Riemannian manifolds of almost nonnegative Ricci curvature
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 39, Page 2085-2090, 2004., 2004 We study the structure of manifolds with almost nonnegative Ricci curvature. We prove a compact Riemannian manifold with bounded curvature, diameter bounded from above, and Ricci curvature bounded from below by an almost nonnegative real number such that the first Betti number havingcodimension two is an infranilmanifold or a finite cover is a sphere ...
Gabjin Yun
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Skew‐symmetric vector fields on a CR‐submanifold of a para‐Kählerian manifold
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 10, Page 535-540, 2004., 2004 We deal with a CR‐submanifold M of a para‐Kählerian manifold M˜, which carries a J‐skew‐symmetric vector field X. It is shown that X defines a global Hamiltonian of the symplectic form Ω on M⊤ and JX is a relative infinitesimal automorphism of Ω. Other geometric properties are given.
Adela Mihai, Radu Rosca
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Screen conformal half‐lightlike submanifolds
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 68, Page 3737-3753, 2004., 2004 We study some properties of a half‐lightlike submanifold M, of a semi‐Riemannian manifold, whose shape operator is conformal to the shape operator of its screen distribution. We show that any screen distribution S(TM) of M is integrable and the geometry of M has a close relation with the nondegenerate geometry of a leaf of S(TM).
K. L. Duggal, B. Sahin
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Constant scalar curvature metrics on connected sums
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 7, Page 405-450, 2003., 2003 The Yamabe problem (proved in 1984) guarantees the existence of a metric of constant scalar curvature in each conformal class of Riemannian metrics on a compact manifold of dimension n ≥ 3, which minimizes the total scalar curvature on this conformal class. Let (M′, g′) and (M″, g″) be compact Riemannian n‐manifolds. We form their connected sumM′#M″ by
Dominic Joyce
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Weakly Noncollapsed RCD Spaces with Upper Curvature Bounds
Analysis and Geometry in Metric Spaces, 2019 We show that if a CD(K, n) space (X, d, f ℋn) with n ≥ 2 has curvature bounded above by κ in the sense of Alexandrov then f is constant.
Kapovitch Vitali, Ketterer Christian
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Super parallel immersions in Euclidean space
International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 1, Page 1-5, 2002., 2002 Two submanifolds of Euclidean n‐space En are called super parallel if the affine normal spaces are homothetic at the corresponding points. Characterizations are given for the action of conformal transformation on super parallel mates. Our notion is generalized to super transnormal submanifolds and its relation with super self‐parallel submanifolds and ...
Tarek Fathy Mersal +1 more
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An introduction to spherical orbit spaces
International Journal of Mathematics and Mathematical Sciences, Volume 32, Issue 8, Page 453-469, 2002., 2002 Consider a compact, connected Lie group G acting isometrically on a sphere Sn of radius 1. Two‐dimensional quotient spaces of the type Sn/G have been investigated extensively. This paper provides an elementary introduction, for nonspecialists, to this important field by way of several classical examples and supplies an explicit list of all the isotropy
Jill Mcgowan, Catherine Searle
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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020 We present some estimate of the Laplacian Spectrum and of Topological Invariants for Riemannian manifold with pinched sectional curvature and with non-empty and non-convex boundary with finite injectivity radius. These estimates do not depend directly on
Sabatini Luca
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