Hyperkähler manifolds with torsion obtained from hyperholomorphic bundles

Mathematical Research Letters

Volumn 10, Issue 4, 2003, Pages 501-513

  Verbitsky, Misha ^a,b  

^a INDEPENDENT UNIVERSITY OF MOSCOW   (Russian Federation)

^b UNIVERSITY OF GLASGOW   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0141637162     PISSN: 10732780     EISSN: None     Source Type: Journal    
DOI: 10.4310/MRL.2003.v10.n4.a9     Document Type: Article

References (24)

1. [Bes] A. Besse, Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 10. Springer-Verlag, Berlin, 1987.
2. [Bo] C. P. Boyer, A note on hyper-Hermitian four-manifolds, Proc. Amer. Math. Soc. 102 (1988), 157-164.
3. [Ca] E. Calabi, Métriques kählériennes et fibrés holomorphes, Ann. Sci. École Norm. Sup. (4) 12 (1979), 269-294.
4. [FG] A. Fino, G. Grantcharov, On some properties of the manifolds with skew-symmetric torsion and holonomy SU(n) and Sp(n), preprint: math.DG/0302358
5. [GP] G. Grantcharov, Y. S. Poon, Geometry of hyper-Kähler connections with torsion, Comm. Math. Phys. 213 (2000), 19-37.
6. [GH] P. Griffiths, J. Harris, Principles of algebraic geometry, Wiley-Intersience, New York, 1978.
7. [GP1] J. Gutowski, G. Papadopoulos, The dynamics of very special black holes, Phys. Lett. B 472 (2000), 45-53.
8. [GP2] _, The moduli spaces of worldvolume brane solitons, Phys. Lett. B 432 (1998), 97-102.
9. [GPS] G. W. Gibbons, G. Papadopoulos, K. S. Stelle, HKT and OKT geometries on soliton black hole moduli spaces, Nuclear Phys. B 508 (1997), 623-658.
10. [HP] P. S. Howe, G. Papadopoulos, Twistor spaces for hyper-Kähler manifolds with torsion, Phys. Lett. B 379 (1996), 80-86.
11. S. Ivanov, Geometry of quaternionic Kähler connections with torsion, J. Geom. Phys. 41 (2002), 235-257; math. DG/0003214
12. [J] D. Joyce, Compact hypercomplex and quaternionic manifolds, J. Differential Geom. 35 (1992), 743-761.
13. [Kob] S. Kobayashi, Differential geometry of complex vector bundles, Princeton University Press, Princeton, NJ, 1987.
14. [Ob] M. Obata, Affine connections on manifolds with almost complex, quaternion or Hermitian structure, Jap. J. Math. 26 (1956), 43-77.
15. [Or] L. Ornea, Weyl structures on quaternionic manifolds. A state of the art, preprint: math.DG/0105041
16. [OPS] L. Ornea, Y. S. Poon, A. Swann, Potential one-forms for hyperkähler structures with torsion, preprint: math.DG/0211427
17. [P] G. Papadopoulos, Brane Solitons and Hypercomplex Structures, Quaternionic structures in mathematics and physics (Rome, 1999), 299-312; math.DG/0003024
18. [PP] H. Pedersen, Y. S. Poon, Inhomogeneous hypercomplex structures on homogeneous manifolds, J. Reine Angew. Math. 516 (1999), 159-181.
19. [V1] M. Verbitsky, Hyperholomorphic bundles over a hyper-Kähler manifold, J. Algebraic Geom. 5 (1996), 633-669; alg-geom/9307008
20. [V2] _, Tri-analytic subvarieties of hyper-Kaehler manifolds, Geom. Funct. Anal. 5 (1995), 92-104; Also available as Hyperkähler embeddings and holomorphic symplectic geometry. II: alg-gaom/9403006
21. [V3] _, Deformations of trianalytic subvarieties of hyper-Kähler manifolds, Selecta Math. (N.S.) 4 (1998), 447-490; alg-geom/9610010
22. [V4] _, Hyperholomorpic connections on coherent sheaves and stability, preprint: math.AG/0107182
23. [V5] _, Protective bundles over hyperkähler manifolds and stability of Fourier-Mukai transform, preprint: math.AG/0107196
24. [V6] _, HyperKähler manifolds with torsion, supersymmetry and Hodge theory, Asian J. Math. 6 (2002), 679-712; math.AG/0112215