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 . They showed B Catherine Searle firstname.lastname@example.org Christine Escher email@example.com Department of Mathematics, Oregon
The Journal of Geometric Analysis – Springer Journals
Published: May 31, 2018
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