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Rigidity of the Weyl chamber flow, and vanishing theorems of Matsushima and Weil

Published online by Cambridge University Press:  01 August 2009

MASAHIKO KANAI
MASAHIKO KANAI*
Affiliation:
Graduate School of Mathematics, Nagoya University, Nagoya, 464-8602, Japan (email: kanai@math.nagoya-u.ac.jp)
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Abstract

The aim of the present paper is to reveal an unforeseen link between the classical vanishing theorems of Matsushima and Weil, on the one hand, and rigidity of the Weyl chamber flow, a dynamical system arising from a higher-rank non-compact Lie group, on the other. The connection is established via ‘transverse extension theorems’: roughly speaking, they claim that a tangential 1-form of the orbit foliation of the Weyl chamber flow that is tangentially closed (and satisfies a certain mild additional condition) can be extended to a closed 1-form on the whole space in a canonical manner. In particular, infinitesimal rigidity of the orbit foliation of the Weyl chamber flow is proved as an application.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 4 , August 2009 , pp. 1273 - 1288
Copyright
Copyright © Cambridge University Press 2009

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