IMPRESSUM   DATENSCHUTZ
	Fakultät für Mathematik	Universität Regensburg
Die folgenden Informationen sind noch nicht freigegeben und deshalb unverbindlich: Differential Geometry II Semester SoSe 2026 Lecturer Claudio Paganini Type of course (Veranstaltungsart) Vorlesung German title Differentialgeometrie II Contents This lecture is a continuation of the differential geometry I course held in WiSe 25/26. The main focus of the course is Lorentzian geometry, with particular emphasis on structures and phenomena relevant to general relativity. Starting from Lorentzian metrics and geodesics, the course develops the theory of causal structures, including causality conditions, and global hyperbolicity. The geometric formulation of the Einstein field equations is introduced, and their implications are explored in the context of explicit solutions to the equations. Accordingly, the Lorentzian part of the course culminates in the study of black hole spacetimes, highlighting their causal and global geometric properties. A secondary part of the course is devoted to symplectic geometry. We will introduce the basic definitions and study some obstructions to the existence of symplectic structures. We aim to understand the constraints symplectic geometry imposes on the underlying manifold. Literature Will be announced on the respective GRIPS page at the start of the semester Recommended previous knowledge Analysis I, II and IV Linear Algebra I and II Differential Geometry I Time/Date Mi 16:00-17:30, D0 14:15-15:45, Do 10-14 Location Mi M 102, Do M 102, Exercises tbd Registration Registration for the exercise classes: In the first week of the semester in the lecture. The formate for the exercises will be the same as in Differential Geometry I. The slots for each team will be assigned in the first week. 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