Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON EINSTEIN HERMITIAN MANIFOLDS II

  • Kim, Jae-Man (DEPARTMENT OF MATHEMATICS EDUCATION KANGWON NATIONAL UNIVERSITY)
  • Published : 2009.03.31
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Abstract

We show that on a Hermitian surface M, if M is weakly *-Einstein and has J-invariant Ricci tensor then M is Einstein, and vice versa. As a consequence, we obtain that a compact *-Einstein Hermitian surface with J-invariant Ricci tensor is $K{\ddot{a}}hler$. In contrast with the 4- dimensional case, we show that there exists a compact Einstein Hermitian (4n + 2)-dimensional manifold which is not weakly *-Einstein.

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References

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