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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Displaying similar documents to “Recursion relations and the asymptotic behavior of the eigenvalues of the laplacian”
The -pseudodifferential calculus on Galois coverings and a higher Atiyah-Patodi-Singer index theorem
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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.
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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...