Examples of vector bundles admitting unique ASD connections on quaternion-Kähler manifolds
HTML articles powered by AMS MathViewer
- by Yasuyuki Nagatomo PDF
- Proc. Amer. Math. Soc. 127 (1999), 3043-3048 Request permission
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
- 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
- N. P. Buchdahl, Instantons on $\textbf {C}\textrm {P}_2$, J. Differential Geom. 24 (1986), no. 1, 19–52. MR 857374
- 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, DOI 10.1063/1.529501
- Claude LeBrun and Simon Salamon, Strong rigidity of positive quaternion-Kähler manifolds, Invent. Math. 118 (1994), no. 1, 109–132. MR 1288469, DOI 10.1007/BF01231528
- M. Mamone Capria and S. M. Salamon, Yang-Mills fields on quaternionic spaces, Nonlinearity 1 (1988), no. 4, 517–530. MR 967469, DOI 10.1088/0951-7715/1/4/002
- Yasuyuki Nagatomo, Vanishing theorem for cohomology groups of $c_2$-self-dual bundles on quaternionic Kähler manifolds, Differential Geom. Appl. 5 (1995), no. 1, 79–97. MR 1319938, DOI 10.1016/0926-2245(95)00008-R
- Y.Nagatomo, Representation theory and ADHM-construction on quaternionic symmetric spaces, a preprint
- Y.Nagatomo, Another type of instanton bundles on $Gr_2(\mathbb C^{n+2})$, to appear in Tokyo J. Math.
- Christian Okonek, Michael Schneider, and Heinz Spindler, Vector bundles on complex projective spaces, Progress in Mathematics, vol. 3, Birkhäuser, Boston, Mass., 1980. MR 561910
- Simon Salamon, Quaternionic Kähler manifolds, Invent. Math. 67 (1982), no. 1, 143–171. MR 664330, DOI 10.1007/BF01393378
- 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, DOI 10.1017/CBO9780511524493
Additional Information
- Yasuyuki Nagatomo
- Affiliation: Institute of Mathematics, University of Tsukuba, Tsukuba-shi, Ibaraki 305-8571, Japan
- Email: nagatomo@math.tsukuba.ac.jp
- 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
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 3043-3048
- MSC (1991): Primary 53C07
- DOI: https://doi.org/10.1090/S0002-9939-99-04977-1
- MathSciNet review: 1616637