Metrics of positive Ricci curvature on quotient spaces
Article
First Online:
- 134 Downloads
- 6 Citations
Keywords
Quotient Space
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.Atiyah, M., Bott, R.: A Lefschetz fixed point formula for elliptic complexes. II. Applications. Ann. Math. 2(88), 451–491 (1968)zbMATHGoogle Scholar
- 2.Aubin, T.: Métriques riemanniennes et courbure. J. Differ. Geom. 4, 383–424 (1970)zbMATHGoogle Scholar
- 3.Back, A., Hsiang, W.Y.: Equivariant geometry and Kervaire spheres. Trans. Am. Math. Soc 304, 207–227 (1987)MathSciNetzbMATHGoogle Scholar
- 4.Bérard Bergery, L.: Certains fibrés à courbure de Ricci positive. C. R. Acad. Sci. Paris 286, 929–931 (1978)zbMATHGoogle Scholar
- 5.Boyer, C., Galicki, K., Nakamaye, M.: Sasakian Geometry, Homotopy Spheres and Positive Ricci Curvature. Preprint, 2002, http://arxiv.org/math.DG/0201147Google Scholar
- 6.Bredon, G.: Introduction to Compact Transformation Groups. Academic Press, New York–London, 1972Google Scholar
- 7.Brieskorn, E.: Beispiele zur Differentialtopologie von Singularitäten. Invent. math. 2, 1–14 (1966)zbMATHGoogle Scholar
- 8.Browder, W.: The Kervaire invariant of framed manifolds and its generalization. Ann. Math. 2(90), 157–186 (1969)zbMATHGoogle Scholar
- 9.Browder, W.: Cobordism invariants, the Kervaire invariant and fixed point free involutions. Trans. Am. Math. Soc. 178, 193–225 (1973)zbMATHGoogle Scholar
- 10.Cheeger, J.: Some examples of manifolds of non-negative curvature. J. Diff. Geom. 8, 623–628 (1973)zbMATHGoogle Scholar
- 11.Dickinson, W.: Curvature properties of the positively curved Eschenburg spaces. Preprint 2000, to appear in Diff. Geom. Appl.Google Scholar
- 12.Ehrlich, P.E.: Metric deformations of curvature, I. Local convex deformations. Geom. Dedicata 5, 1–23 (1976)zbMATHGoogle Scholar
- 13.Eschenburg, J.-H.: Freie isometrische Aktionen auf kompakten Lie-Gruppen mit posi- tiv gekrümmten Orbiträumen. Schriftenreihe des Mathematischen Instituts der Universität Münster (2) 32, Universität Münster, Mathematisches Institut, Münster, 1984Google Scholar
- 14.Fang, W.: Left invariant metrics on simple compact Lie groups and metrics on spheres, thesis, University of Pennsylavania, Philadelphia, USA, 2000Google Scholar
- 15.Fukaya, K., Yamaguchi, T.: The fundamental groups of almost nonnegatively curved manifolds. Ann. Math. 136, 253–333 (1992)MathSciNetzbMATHGoogle Scholar
- 16.Giffen, C.: Desuspendability of free involutions on Brieskorn spheres. Bull. Am. Math. Soc. 75, 426–429 (1969)zbMATHGoogle Scholar
- 17.Giffen, C.: Smooth homotopy projective spaces. Bull. Am. Math. Soc. 75, 509–513 (1969)zbMATHGoogle Scholar
- 18.Giffen, C.: Weakly complex involutions and cobordism of projective spaces. Ann. Math. 2(90), 418–432 (1969)zbMATHGoogle Scholar
- 19.Gilkey, P., Park, J.-H., Tuschmann, W.: Invariant metrics of positive Ricci curvature on principal bundles. Math. Z. 227, 455–463 (1998)MathSciNetzbMATHGoogle Scholar
- 20.Gromoll, D., Meyer, W.: Examples of complete manifolds with positive Ricci curvature. J. Diff. Geom. 21, 195–211 (1985)MathSciNetzbMATHGoogle Scholar
- 21.Gromov, M.: Curvature, diameter and Betti numbers. Comment. Math. Helv. 56, 179–195 (1981)MathSciNetzbMATHGoogle Scholar
- 22.Gromov, M., Lawson, H.B.: Spin and scalar curvature in the presence of a fundamental group I. Ann. Math. 111, 209–230 (1980)MathSciNetzbMATHGoogle Scholar
- 23.Gromov, M., Lawson, H.B.: Positive scalar curvature and the Dirac operator on complete Riemannian manifolds. Publ. Math. I.H.E.S. 58, 295–408 (1983)zbMATHGoogle Scholar
- 24.Grove, K., Verdiani, L., Wilking, B., Ziller, W.: Obstructions to nonnegatively curved metrics in cohomogeneity one. In preparationGoogle Scholar
- 25.Grove, K., Ziller, W.: Curvature and symmetry of Milnor spheres. Ann. Math. 2(152), 331–36 (2000)zbMATHGoogle Scholar
- 26.Grove, K., Ziller, W.: Cohomogeneity one manifolds with positive Ricci curvature. Invent. math. 149, 619–646 (2002)CrossRefMathSciNetzbMATHGoogle Scholar
- 27.Grove, K., Ziller, W.: Vector bundles over ℂP2 with nonnegative curvature. PreprintGoogle Scholar
- 28.Hernandez-Andrade, H.: A class of compact manifolds with positive Ricci curvature. Differential geometry (Proc. Sympos. Pure Math., Vol. XXVII, Stanford Univ., Stanford, Calif., 1973), Part 1, Amer. Math. Soc., Providence, RI, 1975, pp. 73–87Google Scholar
- 29.Hirzebruch, F., Mayer, K.: O(n)-Mannigfaltigkeiten, exotische Sphären und Singu- laritäten. Lecture Notes in Mathematics 57, Springer-Verlag, Berlin-New York, 1968Google Scholar
- 30.Hitchin, N.: Harmonic spinors. Adv. Math. 14, 1–55 (1974)zbMATHGoogle Scholar
- 31.Hsiang, W.-C., Hsiang, W.-Y.: On compact subgroups of the diffeomorphism groups of Kervaire spheres. Ann. Math. 2(85), 359–369 (1967)zbMATHGoogle Scholar
- 32.Iwata, K.: Classifiaction of compact transformation groups on cohomology quaternion projective spaces with codimension one orbits. Osaka J. Math. 15, 475–508 (1978)MathSciNetzbMATHGoogle Scholar
- 33.Kapovitch, V., Ziller, W.: Biquotients with singly generated rational cohomology. Preprint 2002, http://arXiv: math.DG/0210231, to appear in Geometriae DedicataGoogle Scholar
- 34.Lichnerowicz, A.: Spineurs harmoniques. C.R. Acad. Sci. Paris 257, 7–9 (1963)zbMATHGoogle Scholar
- 35.Lopez de Medrano, S.: Involutions on manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete 59, Springer-Verlag, New York-Heidelberg, 1971Google Scholar
- 36.Milnor, J.: Singular points of complex hypersurfaces. Annals of Mathematics Studies, No. 61, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1968Google Scholar
- 37.Montgomery, D., Samelson, H.: Transformation groups of spheres. Ann. Math 44, 454–470 (1943)MathSciNetzbMATHGoogle Scholar
- 38.Müter, M.: Krümmungserhöhende Deformationen mittels Gruppenaktionen, thesis, Westfälische Wilhelms-Universität Münster, Münster, Germany, 1987Google Scholar
- 39.Nash, J.C.: Positive Ricci curvature on fiber bundles. J. Differ Geom 14, 241–254 (1979)MathSciNetzbMATHGoogle Scholar
- 40.Orlik, P.: Smooth homotopy lens spaces. Michigan Math. J. 16, 245–255 (1969)CrossRefzbMATHGoogle Scholar
- 41.Poor, W.A.: Some exotic spheres with positive Ricci curvature. Math. Annalen 216, 245–252 (1975)zbMATHGoogle Scholar
- 42.Rosenberg, J.: C*-algebras, positive scalar curvature, and the Novikov Conjecture, III. Topology 25, 319–336 (1986)CrossRefMathSciNetzbMATHGoogle Scholar
- 43.Schoen, R., Yau, S.-T.: Existence of incompressible minimal surfaces and the topology of three-dimensional manifolds of non-negative scalar curvature. Ann. Math. 110, 127–142 (1979)MathSciNetzbMATHGoogle Scholar
- 44.Schoen, R., Yau, S.-T.: On the structure of manifolds with positive scalar curvature. Manuscripta Math. 28, 159–183 (1979)MathSciNetzbMATHGoogle Scholar
- 45.Schwachhöfer, L., Tuschmann, W.: Almost nonnegative curvature and cohomogeneity one. Max Planck Institute for Mathematics in the Sciences Preprint Series, Preprint no. 62/2001, http://www.mis.mpg.deGoogle Scholar
- 46.Sha, J.-P., Yang, D.-G.: Positive Ricci curvature on the connected sums of Sn× Sm. J. Diff. Geom. 33, 127–137 (1991)MathSciNetzbMATHGoogle Scholar
- 47.Uchida, F.: Classification of compact transformation groups on cohomology complex projective spaces with codimension one orbits. Japan. J. Math. 3, 141–189 (1977)MathSciNetzbMATHGoogle Scholar
- 48.Wall, C.T.C.: Surgery on compact manifolds. London Mathematical Society Monographs 1, Academic Press, London-New York, 1970Google Scholar
- 49.Weinstein, A.: Positively curved deformations of invariant Riemannian metrics. Proc. Am. Math. Soc. 26, 151–152 (1970)zbMATHGoogle Scholar
- 50.Wilking, B.: On fundamental groups of manifolds of nonnegative curvature. Diff. Geom. Appl. 13, 129–165 (2000)CrossRefMathSciNetzbMATHGoogle Scholar
- 51.Witten, E.: Monopoles and four-manifolds. Math. Res. Let. 1, 769–796 (1994)MathSciNetzbMATHGoogle Scholar
- 52.Wraith, D.: Exotic spheres with positive Ricci curvature. J. Diff. Geom. 45, 638–649 (1997)MathSciNetzbMATHGoogle Scholar
- 53.Yau, S.-T.: Calabi’s conjecture and some new results in algebraic geometry. Proc. Nat. Acad. Sci. USA 74, 1798–1799 (1977)zbMATHGoogle Scholar
- 54.Yau, S.-T.: On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation, I. Comm. Pure Appl. Math. 31, 339–41 (1978)MathSciNetzbMATHGoogle Scholar
Copyright information
© Springer-Verlag Berlin Heidelberg 2004