The -pseudodifferential calculus on Galois coverings and a higher Atiyah-Patodi-Singer index theorem
Éric Leichtnam, Paolo Piazza (1997)
Mémoires de la Société Mathématique de France
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Éric Leichtnam, Paolo Piazza (1997)
Mémoires de la Société Mathématique de France
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M. F. Atiyah (1973-1974)
Séminaire Bourbaki
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Werner Müller (1993-1994)
Séminaire Bourbaki
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Zayed, E.M.E. (1997)
International Journal of Mathematics and Mathematical Sciences
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Olivier Biquard, Marc Herzlich, Michel Rumin (2007)
Annales scientifiques de l'École Normale Supérieure
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Gorm Salomonsen (1998)
Journées équations aux dérivées partielles
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I present an alternative way of computing the index of a Dirac operator on a manifold with boundary and a special family of pseudodifferential boundary conditions. The local version of this index theorem contains a number of divergence terms in the interior, which are higher order heat kernel invariants. I will present a way of associating boundary terms to those divergence terms, which are rather local of nature.
Alena Vanžurová, Petra Žáčková (2009)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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We contribute to the reverse of the Fundamental Theorem of Riemannian geometry: if a symmetric linear connection on a manifold is given, find non-degenerate metrics compatible with the connection (locally or globally) if there are any. The problem is not easy in general. For nowhere flat -manifolds, we formulate necessary and sufficient metrizability conditions. In the favourable case, we describe all compatible metrics in terms of the Ricci tensor. We propose an application in the...