On certain curvature conditions on Riemannian manifolds
Ryszard Deszcz, Wiesław Grycak (1990)
Colloquium Mathematicae
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Ryszard Deszcz, Wiesław Grycak (1990)
Colloquium Mathematicae
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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...
Harish Seshadri (2007-2008)
Séminaire de théorie spectrale et géométrie
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We discuss the notion of isotropic curvature of a Riemannian manifold and relations between the sign of this curvature and the geometry and topology of the manifold.
W. Roter (1978)
Colloquium Mathematicae
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Paweł Grzegorz Walczak (1984)
Banach Center Publications
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W. Roter (1977)
Colloquium Mathematicae
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Barbara Opozda (1983)
Annales Polonici Mathematici
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Toshihiko Ikawa, Masahiro Kon (1977)
Colloquium Mathematicae
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Yukio Otsu (1991)
Mathematische Zeitschrift
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Dussan, Martha, Noronha, Maria Helena (2005)
Balkan Journal of Geometry and its Applications (BJGA)
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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.