Results 11 to 20 of about 1,114 (57)
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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Eigenvalues of the basic Dirac operator on quaternion-Kahler foliations [PDF]
, 2006 In this paper, we give an optimal lower bound for the eigenvalues of the basic Dirac operator on a quaternion-Kahler foliation. The limiting case is characterized by the existence of quaternion-Kahler Killing spinors.
Habib, Georges
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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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Quantitative oscillation estimates for almost-umbilical closed hypersurfaces in Euclidean space [PDF]
, 2014 We prove $\epsilon$-closeness of hypersurfaces to a sphere in Euclidean space under the assumption that the traceless second fundamental form is $\delta$-small compared to the mean curvature.
Scheuer, Julian
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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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