AFFINE MANIFOLD WITH MEASURE PRESERVING PROJECTIVE HOLONOMY GROUP

Abstract

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

Keywords

• affine manifold;
• invariant measure;
• Euler characteristic

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References

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