A note on rigidity of 3-Sasakian manifolds
HTML articles powered by AMS MathViewer
- by Henrik Pedersen and Yat Sun Poon PDF
- Proc. Amer. Math. Soc. 127 (1999), 3027-3034 Request permission
Abstract:
Making use of the relations among 3-Sasakian manifolds, hypercomplex manifolds and quaternionic Kähler orbifolds, we prove that complete 3-Sasakian manifolds are rigid.References
- Tadasi Nakayama, On Frobeniusean algebras. I, Ann. of Math. (2) 40 (1939), 611–633. MR 16, DOI 10.2307/1968946
- Walter L. Baily Jr., The decomposition theorem for $V$-manifolds, Amer. J. Math. 78 (1956), 862–888. MR 100103, DOI 10.2307/2372472
- W. L. Baily, On the imbedding of $V$-manifolds in projective space, Amer. J. Math. 79 (1957), 403–430. MR 100104, DOI 10.2307/2372689
- Charles P. Boyer and Krzysztof Galicki, The twistor space of a $3$-Sasakian manifold, Internat. J. Math. 8 (1997), no. 1, 31–60. MR 1433200, DOI 10.1142/S0129167X97000032
- S. K. Singh, On metrical Finsler connections with torsion of generalized Finsler spaces, Indian J. Pure Appl. Math. 25 (1994), no. 4, 399–404. MR 1272811
- Charles P. Boyer, Krzysztof Galicki, and Benjamin M. Mann, The geometry and topology of $3$-Sasakian manifolds, J. Reine Angew. Math. 455 (1994), 183–220. MR 1293878
- Jean-Louis Cathelineau, Déformations équivariantes d’espaces analytiques complexes compacts, Ann. Sci. École Norm. Sup. (4) 11 (1978), no. 3, 391–406 (French). MR 521637, DOI 10.24033/asens.1350
- Roger Godement, Topologie algébrique et théorie des faisceaux, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1252, Hermann, Paris, 1958 (French). Publ. Math. Univ. Strasbourg. No. 13. MR 0102797
- Phillip Griffiths and Joseph Harris, Principles of algebraic geometry, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York, 1978. MR 507725
- N. J. Hitchin, A. Karlhede, U. Lindström, and M. Roček, Hyper-Kähler metrics and supersymmetry, Comm. Math. Phys. 108 (1987), no. 4, 535–589. MR 877637, DOI 10.1007/BF01214418
- Eiji Horikawa, On deformations of holomorphic maps. II, J. Math. Soc. Japan 26 (1974), 647–667. MR 352540, DOI 10.2969/jmsj/02640647
- Shoshichi Kobayashi, Differential geometry of complex vector bundles, Publications of the Mathematical Society of Japan, vol. 15, Princeton University Press, Princeton, NJ; Princeton University Press, Princeton, NJ, 1987. KanĂ´ Memorial Lectures, 5. MR 909698, DOI 10.1515/9781400858682
- Claude LeBrun, A rigidity theorem for quaternionic-Kähler manifolds, Proc. Amer. Math. Soc. 103 (1988), no. 4, 1205–1208. MR 955010, DOI 10.1090/S0002-9939-1988-0955010-7
- Claude LeBrun, Fano manifolds, contact structures, and quaternionic geometry, Internat. J. Math. 6 (1995), no. 3, 419–437. MR 1327157, DOI 10.1142/S0129167X95000146
- Pierre Molino, Riemannian foliations, Progress in Mathematics, vol. 73, Birkhäuser Boston, Inc., Boston, MA, 1988. Translated from the French by Grant Cairns; With appendices by Cairns, Y. Carrière, É. Ghys, E. Salem and V. Sergiescu. MR 932463, DOI 10.1007/978-1-4684-8670-4
- H. Pedersen & Y. S. Poon. Deformations of hypercomplex structures, J. reine angew. Math. 499 (1998), 81–99.
- Simon Salamon, Quaternionic Kähler manifolds, Invent. Math. 67 (1982), no. 1, 143–171. MR 664330, DOI 10.1007/BF01393378
- S. M. Salamon, Differential geometry of quaternionic manifolds, Ann. Sci. École Norm. Sup. (4) 19 (1986), no. 1, 31–55. MR 860810, DOI 10.24033/asens.1503
- Andrew Swann, Hyper-Kähler and quaternionic Kähler geometry, Math. Ann. 289 (1991), no. 3, 421–450. MR 1096180, DOI 10.1007/BF01446581
- Kentaro Yano and Masahiro Kon, Structures on manifolds, Series in Pure Mathematics, vol. 3, World Scientific Publishing Co., Singapore, 1984. MR 794310
Additional Information
- Henrik Pedersen
- Affiliation: Institut for Matematik og Datalogi, Odense Universitet, Campusvej 55, Odense M, DK-5230, Denmark
- Email: henrik@imada.ou.dk
- Yat Sun Poon
- Affiliation: Department of Mathematics, University of California at Riverside, Riverside, California 92521
- Email: ypoon@math.ucr.edu
- Received by editor(s): December 4, 1997
- Published electronically: April 23, 1999
- Additional Notes: The first author was partially supported by NATO CRG-950040. The second author was partially supported by NSF grant DMS-9504908.
- Communicated by: Peter Li
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 3027-3034
- MSC (1991): Primary 53C25; Secondary 32G05, 53C55
- DOI: https://doi.org/10.1090/S0002-9939-99-04889-3
- MathSciNet review: 1605929