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

Nagatomo, Yasuyuki

doi:10.1090/S0002-9939-99-04977-1

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Browser Compatibility Info Help
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
Posted: April 23, 1999
MathSciNet review: 1616637
Full-text PDF Free Access

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.

1. I.N.Bernstein, I.M.Gelfand and S.I.Gelfand, Schubert cells and the cohomology of the spaces , L.M.S.Lecture Notes 69 (1982), Cambridge University Press, 115-140
2. N. P. Buchdahl, Instantons on 𝐶𝑃₂, J. Differential Geom. 24 (1986), no. 1, 19–52. MR 857374 (88b:32066)
3. Krzysztof Galicki and Yat Sun Poon, Duality and Yang-Mills fields on quaternionic Kähler manifolds, J. Math. Phys. 32 (1991), no. 5, 1263–1268. MR 1103479 (92i:53024), http://dx.doi.org/10.1063/1.529501
4. Claude LeBrun and Simon Salamon, Strong rigidity of positive quaternion-Kähler manifolds, Invent. Math. 118 (1994), no. 1, 109–132. MR 1288469 (95k:53059), http://dx.doi.org/10.1007/BF01231528
5. M. Mamone Capria and S. M. Salamon, Yang-Mills fields on quaternionic spaces, Nonlinearity 1 (1988), no. 4, 517–530. MR 967469 (89k:58064)
6. Yasuyuki Nagatomo, Vanishing theorem for cohomology groups of 𝑐₂-self-dual bundles on quaternionic Kähler manifolds, Differential Geom. Appl. 5 (1995), no. 1, 79–97. MR 1319938 (95m:32041), http://dx.doi.org/10.1016/0926-2245(95)00008-R
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. Christian Okonek, Michael Schneider, and Heinz Spindler, Vector bundles on complex projective spaces, Progress in Mathematics, vol. 3, Birkhäuser Boston, Mass., 1980. MR 561910 (81b:14001)
10. Simon Salamon, Quaternionic Kähler manifolds, Invent. Math. 67 (1982), no. 1, 143–171. MR 664330 (83k:53054), http://dx.doi.org/10.1007/BF01393378
11. R. S. Ward and Raymond O. Wells Jr., Twistor geometry and field theory, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, 1990. MR 1054377 (91b:32034)

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|