Torus actions on manifolds of positive sectional curvature.
type: Item
instance of: scholarly article
title: Torus actions on manifolds of positive sectional curvature.
zbMATH Open document ID: 1062.53029
DOI: 10.1007/BF02392966
author: Burkhard Wilking
published in: Acta Mathematica
publication date: 2004-11-15T00:00:00Z
review text: The author proves several new theorems on isometric torus actions on Riemannian manifolds of positive sectional curvature. While these theorems are too complicated to present in the brief space of a review, they represent a significant contribution to the literature. Contents include: an introduction (containing a broad overview of the topic); proof of the connectedness lemma; upper bounds on error-correcting codes; a recognition theorem for the sphere; cyclic group actions with connected fixed-point sets; totally geodesic submanifolds; proof of theorem 2--5; proof of theorem 4; proof of theorem 3; and a bibliography of twenty-seven items.
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C21
zbMATH DE Number: 2115789
zbMATH Keywords: isometric torus actions
zbMATH Keywords: Riemannian manifolds of positive sectional curvature
reviewed by: Joseph D. Zund
MaRDI profile type: Publication
cites work: An infinite family of distinct 7-manifolds admitting positively curved Riemannian structures
cites work: Q3283409
cites work: Q5658847
cites work: Torus actions on homotopy complex projective spaces
cites work: New examples of manifolds with strictly positive curvature
cites work: Homeomorphism classification of positively curved manifolds with almost maximal symmetry rank
cites work: Manifolds with positive curvature
cites work: On the fundamental group of a compact minimal submanifolds
cites work: Geodesics satisfying general boundary conditions
cites work: Positively curved manifolds with maximal symmetry-rank
cites work: Differential topological restrictions by curvature and symmetry
cites work: On the topology of positively curved 4-manifolds with symmetry
cites work: New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities
cites work: Q4146667
cites work: Differentiable Actions of Compact Abelian Lie Groups on S n
cites work: Smooth 𝑆¹ actions on homotopy complex projective spaces and related topics
cites work: Positively curved manifolds with almost maximal symmetry rank
cites work: Theorems of Barth-Lefschetz type and Morse theory on the space of paths
cites work: Q5687301
cites work: Compact homogeneous Riemannian manifolds with strictly positive curvature
cites work: Manifolds with positive sectional curvature almost everywhere.
cites work: Positively curved manifolds with symmetry
description: scientific article; zbMATH DE number 2115789