Strong rigidity of positive quaternion-Kähler manifolds
Article
- 308 Downloads
- 50 Citations
Keywords
Manifold Strong Rigidity
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- 1.Alekseevskii, D.V.: Compact quaternion spaces. Functional Anal. Appl.2, 106–114 (1968)Google Scholar
- 2.Alekseevskii, D.V.: Classification of quaternionic spaces with transitive solvable group of motions. Math. USSR-Izv.9, 297–339 (1975)Google Scholar
- 3.Atiyah, M.F., Singer, I.M.: The index theory of elliptic operators III. Ann. Math.87, 546–604 (1968)Google Scholar
- 4.Bailey, T.N., Eastwood, M.G.: Complex paraconformal manifolds—their differential geometry and twistor theory. Forum Math.3, 61–103 (1991)Google Scholar
- 5.Bando, S., Mabuchi, T.: Uniqueness of Kähler-Einstein metrics modulo connected group actions, in Algebraic Geometry, Sendai, 1985 (Advanced Studies in Pure Math. 10), T. Oda (ed.) North Holland, 1987Google Scholar
- 6.Barker, R., Salamon, S.M.: Analysis on a generalized Heisenberg group. J. London Math. Soc.28, 184–192 (1983)Google Scholar
- 7.Battaglia, F.:S 1 quotients of quaternion-Kähler manifolds (preprint)Google Scholar
- 8.Bérard Bergery, L.: Variétés quaternioniennes, unpublished lecture notes, Espalion, 1979Google Scholar
- 9.Berger, M.: Sur les groupes d'holonomie des variétés à connexion affine et des variétés riemanniennes. Bull. Soc. Math. France83, 279–330 (1955)Google Scholar
- 10.Besse, A.: Einstein Manifolds. Berlin Heidelberg New York: Springer 1987Google Scholar
- 11.Bonan, E.: Sur l'algèbra extérieure d'une variété presque hermitienne quaternionique. C.R. Acad. Sci. Paris295, 115–118 (1982)Google Scholar
- 12.Bott, R.: Non-degenerate critical manifolds. Ann. Math.60, 248–261 (1954)Google Scholar
- 13.Campana, F.: Une version géométrìque généralisée du théorème de produit de Nadel. C.R. Acad. Sci. Paris312, 853–856 (1991)Google Scholar
- 14.de Wit, B., van Proetyen, A.: Special geometry, cubic polynomials and homogeneous space. Commun. Math. Phys.149, 307–333 (1992)Google Scholar
- 15.Fujiki, A.: On the de Rham cohomology group of a compact Kähler symplectic manifold, in Algebraic Geometry, Sendai, 1985 (Advanced Studies in Pure Math. 10), T. Oda (ed.) North Holland, 1987Google Scholar
- 16.Galicki, K.: Multi-centre metrics with negative cosmological constant. Class. Quantum Grav.,8, 1259–1543 (1991)Google Scholar
- 17.Galicki, K., Lawson, H.B.: Quaternionic reduction and quaternionic orbifolds. Math. Ann.282, 1–21 (1988)Google Scholar
- 18.Greub, W., Halperin, S. Vanstone, R.: Curvature, Connections and Characteristic Classes, Volume 3, New York, Academic Press, 1976Google Scholar
- 19.Hartshorne, R.: Algebraic Geometry. Berlin Heidelberg New York: Springer 1977Google Scholar
- 20.Hitchin, N.J.: Kählerian twistor spaces, Proc. Lond. Math. Soc.43, 133–150 (1981)Google Scholar
- 21.Hirzebruch, F.: Topological Methods in Algebraic Geometry, 3rd edition. Berlin Heidelberg New York: Springer 1966Google Scholar
- 22.Hirzebruch, F. Sladowy, P.: Elliptic genera, involutions, and homogeneous spin manifolds. Geom. Dedicata35, 309–343 (1990)Google Scholar
- 23.Kobak, P.Z., Swann, A.: Quaternionic geometry of a nilpotent variety. Math. Ann.197, 747–764 (1993)Google Scholar
- 24.S. Kobayashi: Principal fiber bundles with 1-dimensional toroidal group. Tôhoku Math. J.8, 29–45 (1956)Google Scholar
- 25.Kobayashi, S., Ochiai, T.: Characterization of complex projective spaces and hyperquadrics. J. Math. Kyoto Univ.13, 31–47 (1973)Google Scholar
- 26.Kollár, J., Matsusaka, T.: Riemann-Roch type inequalities. Am. J. Math105, 229–252 (1983)Google Scholar
- 27.Kollár, J., Miyaoka, Y., Mori, S.: Rational connectedness and boundedness of Fano manifolds. J. Differ. Geom.36, 765–779 (1992)Google Scholar
- 28.Kraines, V.: Topology of quaternionic manifolds, Trans. Am. Math. Soc.122, 357–367 (1966)Google Scholar
- 29.LeBrun, C.R.: A rigidity theorem for quaternionic-Kähler manifolds. Proc. Am. Math. Soc.103, 1205–1208 (1988)Google Scholar
- 30.LeBrun, C.R.: Quaternionic-Kähler manifolds and conformal geometry. Math. Ann.284, 353–376 (1989)Google Scholar
- 31.LeBrun, C.R.: On complete quaternionic-Kähler manifolds. Duke Math. J.63, 723–743 (1991)Google Scholar
- 32.LeBrun, C.R.: On the topology of quaternionic manifolds. Twistor Newsletter32, 6–7 (1991)Google Scholar
- 33.Lichnerowicz, A.: Isométries et transformations analytiques d'une variété kählérienne compacte. Bull. Soc. Math. France87, 427–437 (1959)Google Scholar
- 34.Marchiafava, S., Romani, G.: Sui fibrati con struttura quaternionale generalizzata. Ann. Mat. Pura Appl.107, 131–157 (1976)Google Scholar
- 35.Matsusaka, T.: Polarized varieties with a given Hilbert polynomial. Am. J. Math94, 1027–1077 (1972)Google Scholar
- 36.Mori, S.: Hartshorne conjecture and extremal ray. Sugaku Expositions0, 15–37 (1988)Google Scholar
- 37.Nadel, A.: The boundedness of degree of fano varieties with Picard number one. J. Am. Math. Soc.4, 681–692 (1991)Google Scholar
- 38.Nagano, T. Takeuchi, M.: Signature of quaternionic Kaehler manifolds. Proc. Jpn Acad.59, 384–386 (1983)Google Scholar
- 39.Poon, Y.S., Salamon, S.M.: Eight-dimensional quaternionic Kähler manifolds with positive scalar curvature. J. Differ. Geom.33, 363–378 (1991)Google Scholar
- 40.Salamon, S.: Quaternionic Kähler manifolds. Invent. Math.67, 143–171 (1982)Google Scholar
- 41.Salamon, S.: Riemannian Geometry and Holonomy Groups. Pitman Research Notes in Mathematics 201, Longman Scientific, 1989Google Scholar
- 42.Salamon, S.M.: On the cohomology of Kähler and hyper-Kähler manifolds (preprint)Google Scholar
- 43.Swann, A.F.: Hyperkähler and quaternionic Kähler geometry. Math. Ann.289, 421–450 (1991)Google Scholar
- 44.Wang, M.Y.: Parallel spinors and parallel forms. Anal. Global Anal. Geom.7, 59–68 (1989)Google Scholar
- 45.Wiśniewski, J.A.: On Fano manifolds of large index. Manus. Math.70, 145–152 (1991)Google Scholar
- 46.Witten, E.: The index of the Dirac operator in loop space, in Elliptic Curves and Modular Forms in: Algebraic Topology, P.S. Landweber (ed.), Lect. Notes Math. 1326, 161–181 (1988)Google Scholar
- 47.Wolf, J.A.: Complex homogeneous contact structures and quaternionic symmetric spaces. J. Math. Mech.14 1033–1047 (1965)Google Scholar
- 48.Yau, S.T.: On the Ricci-curvature of a complex Kähler manifold and the complex Monge-Ampère equations. Comment. Pure Appl. Math.31, 339–411 (1978)Google Scholar
Copyright information
© Springer-Verlag 1994