## Geometry of Manifolds with Non-negative Sectional Curvature: Editors: Rafael Herrera, Luis Hernández-LamonedaProviding an up-to-date overview of the geometry of manifolds with non-negative sectional curvature, this volume gives a detailed account of the most recent research in the area. The lectures cover a wide range of topics such as general isometric group actions, circle actions on positively curved four manifolds, cohomogeneity one actions on Alexandrov spaces, isometric torus actions on Riemannian manifolds of maximal symmetry rank, n-Sasakian manifolds, isoparametric hypersurfaces in spheres, contact CR and CR submanifolds, Riemannian submersions and the Hopf conjecture with symmetry. Also included is an introduction to the theory of exterior differential systems. |

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### Contents

1 | |

An Introduction to Isometric Group Actions with Applications to Spaces with Curvature Bounded from Below | 20 |

A Note on Maximal Symmetry Rank Quasipositive Curvature and Low Dimensional Manifolds | 45 |

Lectures on nSasakian Manifolds | 56 |

On the Hopf Conjecture with Symmetry | 111 |

An Introduction to Exterior Differential Systems | 117 |

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ˇ ˇ ˇ 4-manifolds action Alexandrov space algebra coboundary operator cohomogeneity one manifolds comodule compact contact form CR submanifold curvature bounded defined definition diffeomorphic dim.D dimension example exterior differential system fiber bundle fibration finite free comodules Geom Geometry Graßmannian Hence homogeneous homomorphism Hopf Hopf conjecture hypersurface integral foliation isometric isoparametric hypersurface isotropy jet bundles jet solution jet,N jetk JetkFM jetkp jXj2 Kähler Lemma linear map manifold with positive Math matrix coefficients maximal symmetry rank metric non-negative numbers partial differential equations polynomial positive curvature positive sectional curvature positively curved manifolds principal curvatures principal orbits Proof quotient Riemannian manifold sectional curvature simply connected smooth maps spectral sequence Spencer cohomology sphere subset subspace Sym"T SymdT SymT tableau A1 tableau comodule Theorem torus totally geodesic vanishes vector fields vector space Young diagram Ziller