Geometriae Dedicata

, Volume 157, Issue 1, pp 367–396

Nonnegatively curved fixed point homogeneous manifolds in low dimensions

Original Paper

Abstract

Let G be a compact Lie group acting isometrically on a compact Riemannian manifold M with nonempty fixed point set MG. We say that M is fixed-point homogeneous if G acts transitively on a normal sphere to some component of MG. Fixed-point homogeneous manifolds with positive sectional curvature have been completely classified. We classify nonnegatively curved fixed-point homogeneous Riemannian manifolds in dimensions 3 and 4 and determine which nonnegatively curved simply-connected 4-manifolds admit a smooth fixed-point homogeneous circle action with a given orbit space structure.

Keywords

Fixed Point Homogeneous Nonnegative Curvature 

Mathematics Subject Classification (2000)

53C20 57S25 51M25 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Maryland at College ParkCollege ParkUSA
  2. 2.Mathematisches InstitutWWU MünsterMünsterGermany

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