Non-negatively Curved 6-Manifolds with Almost Maximal Symmetry Rank

Non-negatively Curved 6-Manifolds with Almost Maximal Symmetry Rank JGeomAnal https://doi.org/10.1007/s12220-018-0026-2 Non-negatively Curved 6-Manifolds with Almost Maximal Symmetry Rank 1 2 Christine Escher · Catherine Searle Received: 16 December 2016 © Mathematica Josephina, Inc. 2018 Abstract We classify closed, simply connected, non-negatively curved 6-manifolds of almost maximal symmetry rank up to equivariant diffeomorphism. Keywords Almost maximal symmetry rank · Equivariant diffeomorphism · 6-Manifolds · Non-negative curvature Mathematics Subject Classification Primary 53C20 · Secondary 57S25 1 Introduction For the class of closed, simply connected Riemannian manifolds, there are no known obstructions that allow us to distinguish between positive and non-negative sectional curvature, in spite of the fact that the number of known examples of manifolds of non-negative sectional curvature is vastly larger than those known to admit a metric of positive sectional curvature. The introduction of symmetries, however, allows us to distinguish between such classes. An important first case to understand is that of maximal symmetry rank, where the symmetry rank is defined to be the rank of the isometry group: symrk(M ) = rk(Isom(M )). For manifolds of strictly positive sectional curvature, a classification up to equivariant diffeomorphism was obtained by Grove and Searle [10]. They showed B Catherine Searle searle@math.wichita.edu Christine Escher tine@math.orst.edu Department of Mathematics, Oregon http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Journal of Geometric Analysis Springer Journals

Non-negatively Curved 6-Manifolds with Almost Maximal Symmetry Rank

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Mathematica Josephina, Inc.
Subject
Mathematics; Differential Geometry; Convex and Discrete Geometry; Fourier Analysis; Abstract Harmonic Analysis; Dynamical Systems and Ergodic Theory; Global Analysis and Analysis on Manifolds
ISSN
1050-6926
eISSN
1559-002X
D.O.I.
10.1007/s12220-018-0026-2
Publisher site
See Article on Publisher Site

Abstract

JGeomAnal https://doi.org/10.1007/s12220-018-0026-2 Non-negatively Curved 6-Manifolds with Almost Maximal Symmetry Rank 1 2 Christine Escher · Catherine Searle Received: 16 December 2016 © Mathematica Josephina, Inc. 2018 Abstract We classify closed, simply connected, non-negatively curved 6-manifolds of almost maximal symmetry rank up to equivariant diffeomorphism. Keywords Almost maximal symmetry rank · Equivariant diffeomorphism · 6-Manifolds · Non-negative curvature Mathematics Subject Classification Primary 53C20 · Secondary 57S25 1 Introduction For the class of closed, simply connected Riemannian manifolds, there are no known obstructions that allow us to distinguish between positive and non-negative sectional curvature, in spite of the fact that the number of known examples of manifolds of non-negative sectional curvature is vastly larger than those known to admit a metric of positive sectional curvature. The introduction of symmetries, however, allows us to distinguish between such classes. An important first case to understand is that of maximal symmetry rank, where the symmetry rank is defined to be the rank of the isometry group: symrk(M ) = rk(Isom(M )). For manifolds of strictly positive sectional curvature, a classification up to equivariant diffeomorphism was obtained by Grove and Searle [10]. They showed B Catherine Searle searle@math.wichita.edu Christine Escher tine@math.orst.edu Department of Mathematics, Oregon

Journal

The Journal of Geometric AnalysisSpringer Journals

Published: May 31, 2018

References

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