Results 11 to 20 of about 1,134 (58)

New Results About the Lambda Constant and Ground States of the 𝑊-Functional

Advanced Nonlinear Studies, 2020
In this paper, we study properties of the lambda constants and the existence of ground states of Perelman’s famous W-functional from a variational formulation. We have two kinds of results.
Ma Li
doaj   +1 more source

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
doaj   +1 more source

The Length of a Shortest Geodesic Loop [PDF]

, 2007
We give a lower bound for the length of a non-trivial geodesic loop on a simply-connected and compact manifold of even dimension with a non-reversible Finsler metric of positive flag curvature. Harris and Paternain use this estimate in their recent paper
Rademacher, Hans-Bert
core   +3 more sources

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
wiley   +1 more source

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
core   +4 more sources

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
wiley   +1 more source

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
wiley   +1 more source

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
wiley   +1 more source

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
wiley   +1 more source

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
doaj   +1 more source