Accession Number : AD0256013

Title :   CURVATURE PROPERTIES OF TEICHMULLER'S SPACE

Corporate Author : HARVARD UNIV CAMBRIDGE MASS

Personal Author(s) : AHLFORS,LARS V.

Report Date : MAR 1961

Pagination or Media Count : 1

Abstract : A point in Teichmuller's space Tg is represented by a closed Riemann surface of fixed genus g(is greater than 1) together with an outer automorphism of its fundamental group. Intrinsic definitions lead to a metric on Tg, introduced by Teichmuller, to a Riemannian structure whose use was suggested by A. Weil, and finally to a complex analytic structure of dimension 3g-3. It was proved by Weil, and with very little computation, it is proved again that the Riemannian metric is Kahlerian with respect to the complex structure. It was reasonable to conjecture that the metric has negative curvature. The main purpose of the work is to verify that the Ricci curvatures are indeed negative. The proof is by explicit computations. (Author)

Descriptors :   *ALGEBRAIC TOPOLOGY, *COMPLEX VARIABLES, *MATHEMATICS

Distribution Statement : APPROVED FOR PUBLIC RELEASE