A Pinching constant for harmonic manifolds

1996/03/25 by K. Ramachandran, Koushik Ramachandran, Ramachandran, K. +2
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities #dg-ga #math.DG

paper · pdf · doi:10.48550/arxiv.dg-ga/9603014

4 pages, latex (e-mail: kram@..., [email protected])

arxiv created 1996/03/25 · arxiv updated 2009/11/30

Abstract

In this note we shall show that the sectional curvature of a harmonic manifold is bounded on both sides. In fact we shall give a pinching constant for all harmonic manifolds. We shall use the imbedding theorem for harmonic manifolds proved by Z.I.Szabo and the description of screw lines in hilbert spaces to prove the result.

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