IMPRESSUM   DATENSCHUTZ
	Fakultät für Mathematik	Universität Regensburg
Die folgenden Informationen sind noch nicht freigegeben und deshalb unverbindlich: Differential Geometry I Semester WiSe 2025 / 26 Lecturer Claudio Paganini 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 semi-Riemannian metrics on manifolds and their curvature. The simplest examples are surfaces in Euclidean space. 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, 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 might be continued in the summer term. Literature https://www.math.uni-potsdam.de/fileadmin/user_upload/Prof-Geometrie/Dokumente/Lehre/Lehrmaterialien/DiffGeo.pdf Recommended previous knowledge Analysis I, II and IV Linear Algebra I and II Time/Date Mo 16:00-17:30, Di 12:30-14:00, Do 10:00 Location Mo M 102, Di M 101, Exercises Do tbd Registration Registration for the exercise classes: In the first week of the semester in the lecture Please register on the GRIPS system as soon as it is available. We will send out additional information and emails via GRIPS Registration for course work/examination/ECTS: FlexNow Course work (Studienleistungen) Successful participation in the exercise classes: Examination (Prüfungsleistungen) Oral exam: Duration: 30 min, Date: individual arrangements, re-exam: Date: Modules BV, MV, MGAGeo, LA-GyGeo ECTS 9