Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Examples of vector bundles
admitting unique ASD connections
on quaternion-Kähler manifolds

Author: Yasuyuki Nagatomo
Journal: Proc. Amer. Math. Soc. 127 (1999), 3043-3048
MSC (1991): Primary 53C07
Published electronically: April 23, 1999
MathSciNet review: 1616637
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove a series of rigidity theorems. Examples of higher rank ASD vector bundles are given on quaternion-Kähler manifolds, which admit the one and only ASD connections modulo the gauge equivalence.

References [Enhancements On Off] (What's this?)

  • 1. I.N.Bernstein, I.M.Gelfand and S.I.Gelfand, Schubert cells and the cohomology of the spaces $G/P$, L.M.S.Lecture Notes 69 (1982), Cambridge University Press, 115-140
  • 2. N.P.Buchdahl, Instantons on $\mathbb CP^2$, J. Differential Geom. 24 (1986), 19-52 MR 88b:32066
  • 3. K.Galicki and Y.S.Poon, Duality and Yang-Mills fields on quaternionic Kähler manifolds, J. Math. Phys. 32 (1991), 1263-1268 MR 92i:53024
  • 4. C.LeBrun and S.M.Salamon, Strong rigidity of positive quaternion-Kähler manifolds, Invent. Math. 118 (1994), 109-132 MR 95k:53059
  • 5. M.Mamone Capria and S.M.Salamon, Yang-Mills fields on quaternionic spaces, Nonlinearity 1 (1988), 517-530 MR 89k:58064
  • 6. Y.Nagatomo, Vanishing theorem for cohomology groups of $c_2$-self-dual bundles on quaternionic Kähler Manifolds, Differential Geom. Appl. 5 (1995), 79-97 MR 95m:32041
  • 7. Y.Nagatomo, Representation theory and ADHM-construction on quaternionic symmetric spaces, a preprint
  • 8. Y.Nagatomo, Another type of instanton bundles on $Gr_2(\mathbb C^{n+2})$, to appear in Tokyo J. Math.
  • 9. C.Okonek, M.Schneider and H.Spindler, ``Vector bundles on complex projective spaces", Progress in Math. 3, Birkhäuser, Boston, (1980) MR 81b:14001
  • 10. S.M.Salamon, Quaternionic Kähler Manifolds, Invent. Math. 67 (1982), 143-171 MR 83k:53054
  • 11. R.S.Ward and R.O.Wells Jr, ``Twistor Geometry and Field Theory", Cambridge monographs on Math. Physics, Cambridge University Press (1989) MR 91b:32034

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 53C07

Retrieve articles in all journals with MSC (1991): 53C07

Additional Information

Yasuyuki Nagatomo
Affiliation: Institute of Mathematics, University of Tsukuba, Tsukuba-shi, Ibaraki 305-8571, Japan

Received by editor(s): October 15, 1997
Received by editor(s) in revised form: December 17, 1997
Published electronically: April 23, 1999
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 1999 American Mathematical Society

American Mathematical Society