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ON EINSTEIN HERMITIAN MANIFOLDS II
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 Title & Authors
ON EINSTEIN HERMITIAN MANIFOLDS II
Kim, Jae-Man;
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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 . 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;;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  crossref(new windwow)
 References
1.
V. Apostolov and P. Gauduchon, The Riemannian Goldberg-Sachs theorem, Internat. J. Math. 8 (1997), no. 4, 421–439 crossref(new window)

2.
Ch. Boyer, Conformal duality and compact complex surfaces, Math. Ann. 274 (1986), no. 3, 517–526 crossref(new window)

3.
E. Calabi and B. Eckmann, A class of compact, complex manifolds which are not algebraic, Ann. of Math. (2) 58 (1953), 494–500 crossref(new window)

4.
J. Kim, On Einstein Hermitian manifolds, Monatsh. Math. 152 (2007), no. 3, 251–254 crossref(new window)

5.
J. Kim, Rigidity theorems for Einstein-Thorpe metrics, Geom. Dedicata 80 (2000), no. 1-3, 281–287