Kyeonghee Jo, Hyuk Kim
Published 2002-10-22Version 1
In this paper, we show that the Euler characteristic of an even dimensional closed projectively flat manifold is equal to the total measure which is induced from a probability Borel measure on RP^n invariant under the holonomy action, and then discuss its consequences and applications. As an application, we show that the Chern's conjecture is true for a closed affinely flat manifold whose holonomy group action permits an invariant probability Borel measure on RP^n; that is, such a closed affinly flat manifold has a vanishing Euler characteristic.
Localizable invariants of combinatorial manifolds and Euler characteristic
The Euler characteristic of an even-dimensional graph
Computing the twisted $L^2$-Euler characteristic
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