Displaying similar documents to “Isotropic curvature: A survey”

Almost-Einstein manifolds with nonnegative isotropic curvature

Harish Seshadri (2010)

Annales de l’institut Fourier

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Let ( M , g ) , n ≥ 4 , be a compact simply-connected Riemannian n -manifold with nonnegative isotropic curvature. Given 0 < l ≤ L , we prove that there exists ε = ε ( l , L , n ) satisfying the following: If the scalar curvature s of g satisfies l ≤ s ≤ L and the Einstein tensor satisfies Ric - s n g ≤ ε then M is diffeomorphic to a symmetric space of compact type. This is related to the result of S. Brendle on the metric rigidity of Einstein manifolds with nonnegative isotropic curvature. ...

Volume comparison theorems for manifolds with radial curvature bounded

Jing Mao (2016)

Czechoslovak Mathematical Journal

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In this paper, for complete Riemannian manifolds with radial Ricci or sectional curvature bounded from below or above, respectively, with respect to some point, we prove several volume comparison theorems, which can be seen as extensions of already existing results. In fact, under this radial curvature assumption, the model space is the spherically symmetric manifold, which is also called the generalized space form, determined by the bound of the radial curvature, and moreover, volume...

g -natural metrics of constant curvature on unit tangent sphere bundles

M. T. K. Abbassi, Giovanni Calvaruso (2012)

Archivum Mathematicum

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We completely classify Riemannian g -natural metrics of constant sectional curvature on the unit tangent sphere bundle T 1 M of a Riemannian manifold ( M , g ) . Since the base manifold M turns out to be necessarily two-dimensional, weaker curvature conditions are also investigated for a Riemannian g -natural metric on the unit tangent sphere bundle of a Riemannian surface.