Torus actions on manifolds of positive sectional curvature

By Burkhard Wilking. 2003

130 citations recorded by the source corpus.

or equivMently as the largest number d such tha t a d-dimensional torus acts effectively and isometrically on M. Grove and Searle [13] showed tha t symrank((M,g))~< [ 89 provided tha t M is a compact manifold of positive sectional curvature. They also studied the case of equali ty and showed tha t this can only occur if the under lying manifold is diffeomorphic to C P n, S ~, or to a lens space. Our main new tool is the following basic result.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/82e5b0dec464e69111adacbeac9a14d8ef40250c

How researchers see this paper

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In Applied Mathematics

1. Burkhard Wilking
2. F. Fang
3. L. Verdiani
4. Xiaochun Rong
5. W. Ziller
6. W. Wylie
7. K. Grove
8. Peter Petersen

In Geometry and Topology

1. Burkhard Wilking
2. F. Fang
3. L. Verdiani
4. Xiaochun Rong
5. W. Ziller
6. W. Wylie
7. K. Grove
8. Peter Petersen

Citations in the corpus

• Homeomorphism classification of positively curved manifolds with almost maximal symmetry rank (2003, background): “[FMR], [FR2,3], [GS], [Hi], [HK], [PS], [Ro1], [ Wi ], [Ya], etc).”
• Cohomogeneity One Manifolds of Even Dimension with Strictly Positive Sectional Curvature (2004, background): “Recently, very strong results on the topology of compact positively curved manifolds M have been proved by Wilking [30], [31], [32] assuming the existence of totally geodesic submanifolds of small codimension.”
• Nonnegatively and Positively curved manifolds (2007, methodology): “Recently, the author made the following basic observation, see [Wilking, 2003].”