In this paper, we show that the Euler characteristic of an even dimensionalclosed projectively flat manifold is equal to the total measure which isinduced from a probability Borel measure on RP^n invariant under the holonomyaction, and then discuss its consequences and applications. As an application,we show that the Chern's conjecture is true for a closed affinely flat manifoldwhose holonomy group action permits an invariant probability Borel measure onRP^n; that is, such a closed affinly flat manifold has a vanishing Eulercharacteristic.
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