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On isometries of the carathéodory and Kobayashi metrics on strongly pseudoconvex domains

Harish Seshadri — 2006

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let Ω 1 and Ω 2 be strongly pseudoconvex domains in n and f : Ω 1 Ω 2 an isometry for the Kobayashi or Carathéodory metrics. Suppose that f extends as a C 1 map to Ω ¯ 1 . We then prove that f | Ω 1 : Ω 1 Ω 2 is a CR or anti-CR diffeomorphism. It follows that Ω 1 and Ω 2 must be biholomorphic or anti-biholomorphic.

Almost-Einstein manifolds with nonnegative isotropic curvature

Harish Seshadri — 2010

Annales de l’institut Fourier

Let ( M , g ) , n 4 , be a compact simply-connected Riemannian n -manifold with nonnegative isotropic curvature. Given 0 < l L , we prove that there exists ε = ε ( l , L , n ) satisfying the following: If the scalar curvature s of g satisfies l s L and the Einstein tensor satisfies Ric - s n g ε then M is diffeomorphic to a symmetric space of compact type. This is related to the result of S. Brendle on the metric rigidity of Einstein manifolds with nonnegative isotropic curvature.

Isotropic curvature: A survey

Harish Seshadri

Séminaire de théorie spectrale et géométrie

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.

Absolute Riesz summability

Prem Chandra — 1975

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Si generalizzano due teoremi dovuti all'Autore sulle serie di Fourier.

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