대한수학회지 (Journal of the Korean Mathematical Society)

  • 제40권1호
  • /
  • Pages.109-128
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  • 2003
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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INVARIANT MEASURE AND THE EULER CHARACTERISTIC OF PROJECTIVELY ELAT MANIFOLDS

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

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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참고문헌

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피인용 문헌

  1. The analytic continuation of hyperbolic space vol.161, pp.1, 2012, https://doi.org/10.1007/s10711-012-9698-0