Torus actions and positive and non-negative curvature

  • We investigate questions concerning symmetries and Riemannian metrics of positive or non-negative curvature. To be more precise, we discuss the question if a non-trivial circle action on a manifold implies the existence of an (invariant) metric of positive scalar curvature. Moreover, we classify those simply-connected torus manifolds which admit an invariant metric of non-negative sectional curvature. First results concerning the homotopy type of the moduli space of invariant metrics of positive scalar curvature on a quasitoric manifold are also presented. Here a torus manifold is an even-dimensional manifold with an effective action of a half-dimensional torus which has fixed points. Quasitoric manifolds are special torus manifolds with an orbit space diffeomorphic to a simple convex polytope.

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Metadaten
Author:Michael Wiemeler
URN:urn:nbn:de:bvb:384-opus4-42808
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/4280
Advisor:Bernhard Hanke
Type:Habilitation
Language:English
Publishing Institution:Universität Augsburg
Granting Institution:Universität Augsburg, Mathematisch-Naturwissenschaftlich-Technische Fakultät
Date of final exam:2017/05/10
Release Date:2017/06/19
GND-Keyword:Positive Krümmung; Nichtnegative Krümmung; Riemannsche Metrik; Mannigfaltigkeit; Torus
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):Deutsches Urheberrecht