Relations between metrics of almost positive curvature on the Gromoll-Meyer sphere
HTML articles powered by AMS MathViewer
- by Owen Dearricott PDF
- Proc. Amer. Math. Soc. 140 (2012), 2169-2178 Request permission
Abstract:
We give a simplified proof that Wilhelm’s metric on the Gromoll-Meyer sphere has positive curvature almost everywhere. We determine that its zero locus coincides with that of the almost positively curved metric of Eschenburg and Kerin.References
- Jeff Cheeger, Some examples of manifolds of nonnegative curvature, J. Differential Geometry 8 (1973), 623–628. MR 341334
- Jost-Hinrich Eschenburg, Freie isometrische Aktionen auf kompakten Lie-Gruppen mit positiv gekrümmten Orbiträumen, Schriftenreihe des Mathematischen Instituts der Universität Münster, 2. Serie [Series of the Mathematical Institute of the University of Münster, Series 2], vol. 32, Universität Münster, Mathematisches Institut, Münster, 1984 (German). MR 758252
- J.-H. Eschenburg and M. Kerin, Almost positive curvature on the Gromoll-Meyer sphere, Proc. Amer. Math. Soc. 136 (2008), no. 9, 3263–3270. MR 2407092, DOI 10.1090/S0002-9939-08-09429-X
- Detlef Gromoll and Wolfgang Meyer, An exotic sphere with nonnegative sectional curvature, Ann. of Math. (2) 100 (1974), 401–406. MR 375151, DOI 10.2307/1971078
- Barrett O’Neill, The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 459–469. MR 200865
- Frederick Wilhelm, An exotic sphere with positive curvature almost everywhere, J. Geom. Anal. 11 (2001), no. 3, 519–560. MR 1857856, DOI 10.1007/BF02922018
- Burkhard Wilking, Manifolds with positive sectional curvature almost everywhere, Invent. Math. 148 (2002), no. 1, 117–141. MR 1892845, DOI 10.1007/s002220100190
Additional Information
- Owen Dearricott
- Affiliation: Department of Mathematics, University of California, Riverside, Riverside, California 92521
- Address at time of publication: Department of Mathematics, University of California, Los Angeles, Box 951555, Los Angeles, California 90095-1555
- Email: owend@ucr.edu
- Received by editor(s): November 10, 2010
- Received by editor(s) in revised form: February 1, 2011
- Published electronically: October 12, 2011
- Communicated by: Chuu-Lian Terng
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 2169-2178
- MSC (2010): Primary 53C21
- DOI: https://doi.org/10.1090/S0002-9939-2011-11056-6
- MathSciNet review: 2888202