Displaying similar documents to “Some geometry and combinatorics for the S -invariant of ternary cubics.”

The evolution of the scalar curvature of a surface to a prescribed function

Paul Baird, Ali Fardoun, Rachid Regbaoui (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We investigate the gradient flow associated to the prescribed scalar curvature problem on compact riemannian surfaces. We prove the global existence and the convergence at infinity of this flow under sufficient conditions on the prescribed function, which we suppose just continuous. In particular, this gives a uniform approach to solve the prescribed scalar curvature problem for general compact surfaces.

Non-negative curvature obstructions in cohomogeneity one and the Kervaire spheres

Karsten Grove, Luigi Verdiani, Burkhard Wilking, Wolfgang Ziller (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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In contrast to the homogeneous case, we show that there are compact cohomogeneity one manifolds that do not support invariant metrics of non-negative sectional curvature. In fact we exhibit infinite families of such manifolds including the exotic Kervaire spheres. Such examples exist for any codimension of the singular orbits except for the case when both are equal to two, where existence of non-negatively curved metrics is known.

On some type of curvature conditions

Mohamed Belkhelfa, Ryszard Deszcz, Małgorzata Głogowska, Marian Hotloś, Dorota Kowalczyk, Leopold Verstraelen (2002)

Banach Center Publications

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In this paper we present a review of recent results on semi-Riemannian manifolds satisfying curvature conditions of pseudosymmetry type.

Isotropic curvature: A survey

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.

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.