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Differential geometry II SemesterSoSe 2022 Lecturer Ulrich Bunke Type of course (Veranstaltungsart) Vorlesung German title Differentialgeometrie II Contents In this second part of the course we will investigate Riemannian manifolds in greater detail. We study how properties of the curvature tensor determine global properties of the Riemannian manifold as a metric space. In particular we will show Hadamard's theorem stating that negatively curved simply connected complete manifolds are homeomorphic to Euclidean spaces and that complete manifolds with positive Ricci-curvature have bounded diameter. We will consider symmetric spaces as an interesting class of examples of Riemannian manifolds. We will also consider further geometric structures on Riemannian manifolds, e.g. complex structures. If time permits we will do first steps towards global analysis by considering properties of the Laplace operator. The parallel seminar on Morse theory might be an interesting add-on for participants of the course. Literature Will be given in the lecture course. Recommended previous knowledge manifolds and Riemannian metrics fibre bundle language connections on vector bundles Time/Date Mo, Do 10-12 Location MA 102 Course homepage GRIPS (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration
BV, MV, MGAGeo, LA-GyGeo ECTS 9 |