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In this manuscript we provide new extensions for the Myers theorem in weighted Riemannian and Lorentzian manifolds. As application we obtain a closure theorem for spatial hypersurfaces immersed in some time-like manifolds.

Comparing heat operators through local isometries or fibrations

Manlio Bordoni (2000)

Bulletin de la Société Mathématique de France

Comparision of the length of infinite geodesics in manifolds with nonpositive curvature.

Thórdur Jónsson (1982)

Mathematica Scandinavica

Comparison theorems and hypersurfaces.

J.-H. Eschenburg (1987)

Manuscripta mathematica

Comparison theorems for compact symmetric spaces

Min-Oo, Ernst A. Ruh (1979)

Annales scientifiques de l'École Normale Supérieure

Comparison Theory for Riccati equations.

E. Heintze, J.-H. Eschenburg (1990)

Manuscripta mathematica

Complete gradient Ricci solitons

Udo Simon (2015)

Colloquium Mathematicae

For complete gradient Ricci solitons we state necessary conditions for a non-trivial soliton structure in terms of intrinsic curvature invariants.

Complete Homogeneous Riemannian Manifolds of Negative Sectional Curvature.

Su-Shing Chen (1975)

Commentarii mathematici Helvetici

Complete Kähler Manifolds of Positive Ricci Curvature.

Sai-Kee Yeung (1990)

Mathematische Zeitschrift

Complete Riemannian manifolds admitting a pair of Einstein-Weyl structures

Amalendu Ghosh (2016)

Mathematica Bohemica

We prove that a connected Riemannian manifold admitting a pair of non-trivial Einstein-Weyl structures $(g, \pm ω)$ with constant scalar curvature is either Einstein, or the dual field of $ω$ is Killing. Next, let $(M^{n}, g)$ be a complete and connected Riemannian manifold of dimension at least $3$ admitting a pair of Einstein-Weyl structures $(g, \pm ω)$ . Then the Einstein-Weyl vector field $E$ (dual to the $1$ -form $ω$ ) generates an infinitesimal harmonic transformation if and only if $E$ is Killing.

Complete spacelike hypersurfaces with constant scalar curvature

Schi Chang Shu (2008)

Archivum Mathematicum

In this paper, we characterize the $n$ -dimensional $(n \geq 3)$ complete spacelike hypersurfaces $M^{n}$ in a de Sitter space $S_{1}^{n + 1}$ with constant scalar curvature and with two distinct principal curvatures one of which is simple.We show that $M^{n}$ is a locus of moving $(n - 1)$ -dimensional submanifold $M_{1}^{n - 1} (s)$ , along $M_{1}^{n - 1} (s)$ the principal curvature $λ$ of multiplicity $n - 1$ is constant and $M_{1}^{n - 1} (s)$ is umbilical in $S_{1}^{n + 1}$ and is contained in an $(n - 1)$ -dimensional sphere $S^{n - 1} (c (s)) = E^{n} (s) \cap S_{1}^{n + 1}$ and is of constant curvature ${(\frac{d {log | λ^{2} - (1 - R) |^{1 / n}}}{d s})}^{2} - λ^{2} + 1$ ,where $s$ is the arc length of an orthogonal trajectory of the family...

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