• Jo, Kyeong-Hee (School of Mathematical Sciences Seoul National University) ;
  • Kim, Hyuk (School of Mathematical Sciences Seoul National University)
  • Published : 2003.01.01


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 Chen'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.



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