Four-Dimensional Almost Kähler Einstein and *-Einstein Manifolds

Geometriae Dedicata

Volumn 69, Issue 1, 1998, Pages 91-112

  Oguro, Takashi ^a   Sekigawa, Kouei ^b  

^a TOKYO DENKI UNIVERSITY   (Japan)

^b NIIGATA UNIVERSITY   (Japan)

Author keywords

* Einstein manifolds; Almost K hler manifolds; K hler manifolds; Weakly * Einstein manifolds

Indexed keywords

EID: 0002122744     PISSN: 00465755     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1005005526324     Document Type: Article

References (20)

1. Bonome, A., Castro, R., Gracia-Rio, E., Hervella, L. M. and Matsushita, Y.: The Kähler-Einstein metrics on a K3 surface cannot be almost Kähler with respect to an opposite almost complex structure, Kodai Math. J. 18 (1995), 506-514.
2. Cordero, L. A., Fernandez, M. and de Leou, M.: Examples of compact non-Kähler almost Kähler manifolds, Proc. Amer. Math. Soc. 95 (1985), 280-286.
3. Draghici, T.: On the almost Kähler manifolds with Hermitian Ricci tensor, Houston J. Math. 20 (1994), 293-298.
4. Draghici, T.: On some 4-dimensional almost Kähler manifolds, Kodai Math. J. 18 (1995), 156-168.
5. Goldberg, S. I.: Integrability of almost Kähler manifolds, Proc. Amer. Math. Soc. 21 (1969), 96-100.
6. Gray, A.: Curvature identities for Hermitian and almost Hermitian manifolds, Tôhoku Math. J. 28 (1969), 601-612.
7. Gray, A. and Hervella, L. M.: The sixteen classes of almost Hermitian manifolds and their linear invariants, Ann. Mat. Pura Appl. 123 (1980), 35-58.
8. Hitchin, N.: Compact four-dimensional Einstein manifolds, J. Differential Geom. 9 (1974), 435-441.
9. Jelonek, W.: Some simple examples of almost Kähler non-Kähler structures, Math. Ann. 305 (1996), 639-649.
10. Libermann, P.: Classification and conformal properties of almost Hermitian structures, János Bolyai 31, Diff. Geom. Budapest (Hungary), (1979), 371-391.
11. Matsushita, Y.: Some remarks on fields of 2-planes on compact smooth 4-manifolds, Adv. Stud. Pure Math., Academic Press 22 (1993).
12. Murakoshi, N., Oguro, T. and Sekigawa, K.: Four-dimensional almost Kähler locally symmetric spaces, Differential Geom. Appl. 6 (1996), 237-244.
13. Oguro, T.: On almost Kähler manifolds of constant curvature, Tsukuba J. Math. 21 (1997) (to appear).
14. Oguro, T. and Sekigawa, K.: Non-existence of almost Kähler structure on hyperbolic spaces of dimension 2n(≥ 4), Math. Ann. 300 (1994), 317-329.
15. Oguro, T. and Sekigawa, K.: Almost Kähler structures on the Riemannian product of a 3-dimensional hyperbolic space and a real line, Tsukuba J. Math. 20 (1996), 151-161.
16. Sekigawa, K.: On some 4-dimensional compact almost Hermitian manifolds, J. Ramanujan Math. Soc. 2 (1987), 101-116.
17. Sekigawa, K.: On some compact Einstein almost Kähler manifolds, J. Math. Soc. Japan 39 (1987), 677-684.
18. Sekigawa, K. and Vanhecke, L.: Four-dimensional almost Kähler Einstein manifolds, Ann. Math. Pura Appl. 157 (1990), 149-160.
19. Thurston, W. P.: Some simple examples of symplectic manifolds, Proc. Amer. Math. Soc. 55 (1976), 467-468.
20. Yano, K.: Differential Geometry on Complex and Almost Complex Spaces, New York, Pergamon Press, 1965.