Vanishing theorems on Hermitian manifolds

Differential Geometry and its Application

Volumn 14, Issue 3, 2001, Pages 251-265

  Alexandrov, Bogdan ^a   Ivanov, Stefan ^a  

^a UNIVERSITY OF SOFIA   (Bulgaria)

Author keywords

53C15; 53C55; Bismut connection; Dolbeault operator; Hermitian manifold; KT manifolds; Rational surface; Weyl structure

Indexed keywords

EID: 0000288390     PISSN: 09262245     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0926-2245(01)00044-4     Document Type: Article

References (24)

1. B. Alexandrov, S. Ivanov, Weyl structures with positive Ricci tensor, Preprint ICTP, IC/99/156.
2. Barth W., Peters C., Van de Ven A. Compact Complex Surfaces. 1984;Springer, Berlin.
3. Besse A. Einstein Manifolds. 1987;Springer, New York.
4. Bismut J.-M. A local index theorem for non-Kähler manifolds. Math. Ann. 284:1989;681-699.
5. Borel A. A spectral sequence for complex analytic bundles, Appendix II. Hirzerbruch. Topological Methods in Algebraic Geometry. 1996;202-217 Springer, New York.
6. Bott R. Homogeneous vector bundles. Ann. of Math. 66:1957;203-248.
7. Gates S.J., Hul C.M., Roček M. Twisted multiplets and new supersymmetric non-linear σ -models. Nuclear Phys. B. 248:1984;157-186.
8. Gauduchon P. Le theoreme de l'excentricité nulle. C.R. Acad. Sci. Paris Ser. A. 285:1977;387-390.
9. Gauduchon P. Fibrés hermitiens à endomorphisme de Ricci non-négatif. Bull. Soc. Math. France. 105:1977;113-140.
10. Gauduchon P. La 1-forme de torsion d'une variété hermitienne compacte. Math. Ann. 267:1984;495-518.
11. Gauduchon P. Hermitian connections and Dirac operators. Boll. Un. Mat. Ital. B. 11:1997;. (7) suppl. 2, 257-289.
12. Gauduchon P., Ivanov S. Einstein-Hermitian surfaces and Hermitian Einstein-Weyl structures in dimension 4. Math. Z. 226:1997;317-326.
13. G. Grantcharov, private communication.
14. Hitchin N. Harmonic spinors. Advances in Math. 14:1974;1-55.
15. Howe P.S., Papadopoulos G. Finitness and anomalies in (4,0) supersymmetric sigma models. Nuclear Phys. B. 381:1992;360-372.
16. Howe P.S., Papadopoulos G. Twistor spaces for hyper-Kähler manifolds with torsion. Phys. Lett. B. 379:1996;81-86.
17. Michelson M.L. On the existence of special metrics in complex geometry. Acta Math. 143:1983;261-295.
18. Opfermann A., Papadopoulos G. Homogeneous HKT and QKT manifolds. math-ph/9807026.
19. Pittie H. The Dolbeault-cohomology ring of a compact, even-dimensional Lie group. Proc. Indian Acad. Sci. Math. Sci. 98:1988;117-152.
20. Samelson H. A class of complex analytic manifolds. Portugaliae Math. 12:1953;129-132.
21. Spindel P., Sevrin A., Troost W., van Proeyen A. Extended supersymmetric σ -models on group manifolds. Nuclear Phys. B. 308:1988;662-698.
22. Tsukada K. Holomorphic forms and holomorphic vector fields on compact generalized Hopf manifolds. Compositio Math. 93:1994;1-22.
23. Vaisman I. On locally conformal almost Kähler manifolds. Israel J. Math. 24:1976;338-351.
24. Vaisman I. A survey of generalized Hopf manifolds. Rend. Sem. Mat. Univ. Politec. Torino. 1983;205-221.