Hermitian $*$-Einstein surfaces
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- by Geo Grantcharov and Oleg Muškarov PDF
- Proc. Amer. Math. Soc. 120 (1994), 233-239 Request permission
Abstract:
We study the problem when a compact Hermitian ${\ast }$-Einstein surface $M$ is Kählerian and show that it is true if $M$ is additionally assumed to be either Einstein or anti-self-dual. We also prove that if the ${\ast }$-scalar curvature of $M$ is positive then $M$ is a conformally Kähler surface with positive first Chern class.References
- Arthur L. Besse, Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 10, Springer-Verlag, Berlin, 1987. MR 867684, DOI 10.1007/978-3-540-74311-8
- Andrzej Derdziński, Self-dual Kähler manifolds and Einstein manifolds of dimension four, Compositio Math. 49 (1983), no. 3, 405–433. MR 707181
- S. I. Goldberg, Integrability of almost Kaehler manifolds, Proc. Amer. Math. Soc. 21 (1969), 96–100. MR 238238, DOI 10.1090/S0002-9939-1969-0238238-1
- Alfred Gray, Curvature identities for Hermitian and almost Hermitian manifolds, Tohoku Math. J. (2) 28 (1976), no. 4, 601–612. MR 436054, DOI 10.2748/tmj/1178240746
- Takashi Koda, Self-dual and anti-self-dual Hermitian surfaces, Kodai Math. J. 10 (1987), no. 3, 335–342. MR 929993, DOI 10.2996/kmj/1138037464
- Zbigniew Olszak, A note on almost Kaehler manifolds, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 26 (1978), no. 2, 139–141 (English, with Russian summary). MR 493830
- Zbigniew Olszak, On the existence of generalized complex space forms, Israel J. Math. 65 (1989), no. 2, 214–218. MR 998671, DOI 10.1007/BF02764861
- Kouei Sekigawa, On some compact Einstein almost Kähler manifolds, J. Math. Soc. Japan 39 (1987), no. 4, 677–684. MR 905633, DOI 10.2969/jmsj/03940677
- Kouei Sekigawa, On some $4$-dimensional compact almost Hermitian manifolds, J. Ramanujan Math. Soc. 2 (1987), no. 2, 101–116. MR 945613
- K. Sekigawa and L. Vanhecke, Four-dimensional almost Kähler Einstein manifolds, Ann. Mat. Pura Appl. (4) 157 (1990), 149–160. MR 1108474, DOI 10.1007/BF01765316
- Franco Tricerri and Lieven Vanhecke, Curvature tensors on almost Hermitian manifolds, Trans. Amer. Math. Soc. 267 (1981), no. 2, 365–397. MR 626479, DOI 10.1090/S0002-9947-1981-0626479-0
- Izu Vaisman, On locally and globally conformal Kähler manifolds, Trans. Amer. Math. Soc. 262 (1980), no. 2, 533–542. MR 586733, DOI 10.1090/S0002-9947-1980-0586733-7
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 233-239
- MSC: Primary 53C25; Secondary 53C55
- DOI: https://doi.org/10.1090/S0002-9939-1994-1186132-9
- MathSciNet review: 1186132