Affine manifold with measure preserving projective holonomy groups

Kyeongsu Park

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Bull. Korean Math. Soc. 2001; 38(1): 157-161

Printed March 1, 2001

Affine manifold with measure preserving projective holonomy groups

Kyeongsu Park

Jeonju University

Abstract

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Abstract

In this paper, we prove that an affine manifold $M$ is finitely covered by a manifold $\bar M$ where $\bar M$ is radiant or the tangent bundle of $\bar M$ has a conformally flat vector subbundle if the projective holonomy group of $M$ admits an invariant probability Borel measure. This implies that $\chi(M)$ is zero.

Keywords: affine manifold, invariant measure, Euler characteristic

MSC numbers: 53C15, 57N16