ON EINSTEIN HERMITIAN MANIFOLDS II

Title & Authors
ON EINSTEIN HERMITIAN MANIFOLDS II
Kim, Jae-Man;

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 $\small{K{\ddot{a}}hler}$. 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.
Keywords
Hermitian surface;weakly *-Einstein;J-invariant Ricci tensor;Einstein;vice versa;*-Einstein;$\small{K{\ddot{a}}hler}$;compact Einstein Hermitian (4n + 2)-dimensional manifold;
Language
English
Cited by
1.
Remarks on Einstein-like Hermitian manifolds, Periodica Mathematica Hungarica, 2010, 60, 1, 71
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