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A second derivative formula of the Liouville entropy atspaces of constant negative curvature

Published online by Cambridge University Press:  12 April 2001

GERHARD KNIEPER
GERHARD KNIEPER
Affiliation:
Institut für Mathematik, Universität Augsburg, 86135 Augsburg, Germany
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Abstract

In this paper we study a new functional on the space of metricswith negative curvature on a compact manifold. It is a linearcombination of Liouville entropy and total scalar curvature.Locally symmetric spaces are critical points of this functional.We provide an explicit formula for its second derivative atmetrics of constant negative curvature. In particular, this showsthat a metric of constant curvature is a local maximum.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 17 , Issue 5 , October 1997 , pp. 1131 - 1135
Copyright
1997 Cambridge University Press

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