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Differential Geometry I SemesterWiSe 2023 / 24 Lecturer Bernd Ammann Type of course (Veranstaltungsart) Vorlesung German title Differentialgeometrie I Contents This lecture is an introduction to differential geometry, more precisely to semi-Riemannian manifolds, their curvature and global properties. The main topic are Riemannian metrics on manifolds. The simplest examples are surfaces in Euclidean space ℝ3. Such surfaces may be intrinsically curved, as e.g. the sphere. Or they may only be extrinsically curved, as e.g. a cylinder -- which may be cut by a "scissor" and then this surface is isometric to an open set of a plane. The goal is to understand not only surfaces, but similar curvature quantities in arbitrary dimensions and codimensions, a generalization going back to work of Bernhard Riemann. Very similar structures were later used by Einstein and others in order to get a mathematical framework to describe general relativity. The theory is still a very active area in mathematics and theoretical physics. The lecture will be continued in the summer term. Literature C. Bär, Differential Geometry, Unpublished Lecture Notes, to access click on this link, Further literature on the web page Recommended previous knowledge
Time/Date Monday and Friday, 10-12 Location M102 Course homepage https://ammann.app.uni-regensburg.de/lehre/2023w_diffgeo1 (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration
BV, MV, MGAGeo, LA-GyGeo ECTS 9 |