Displaying similar documents to “On certain curvature conditions on Riemannian manifolds”

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...

Unit tangent sphere bundles with constant scalar curvature

Eric Boeckx, Lieven Vanhecke (2001)

Czechoslovak Mathematical Journal

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As a first step in the search for curvature homogeneous unit tangent sphere bundles we derive necessary and sufficient conditions for a manifold to have a unit tangent sphere bundle with constant scalar curvature. We give complete classifications for low dimensions and for conformally flat manifolds. Further, we determine when the unit tangent sphere bundle is Einstein or Ricci-parallel.