On the eta invariant, stable positive scalar curvature, and Higher -genera.
Bousaidi, M.A. (2001)
Lobachevskii Journal of Mathematics
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Bousaidi, M.A. (2001)
Lobachevskii Journal of Mathematics
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Andrzej Derdziński (1988)
Bulletin de la Société Mathématique de France
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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.
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.
Sun-Yung A. Chang, Matthew J. Gursky, Paul C. Yang (2003)
Publications Mathématiques de l'IHÉS
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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.
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.
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.