2025/2026
Картанова геометрия
Статус:
Дисциплина общефакультетского пула
Кто читает:
Факультет математики
Где читается:
Факультет математики
Когда читается:
1, 2 модуль
Охват аудитории:
для всех кампусов НИУ ВШЭ
Преподаватели:
Ма Тяньюй
Язык:
английский
Контактные часы:
60
Course Syllabus
Abstract
This course provides an introduction to Cartan geometry, as well as its applications. Cartan geometry establishes the relationship between a geometric structure of finite-type and the symmetries (e.g., infinitesimal automorphism) of this geometric structure. This approach allows applying theory in Lie algebra representation theory to study differential geometric structures.
The course starts with a review of the basic notions and theorems in differential geometry, followed by the Klein geometry (Homogeneous model spaces of Cartan geometries). Then we will focus on the basic notions and theorems in the general Cartan geometry. Applications and examples of classical Cartan bundles will be discussed. Finally, an elementary introduction to parabolic Cartan geometry will be provided.
Learning Objectives
- 1. Understand the basic notions in Cartan geometry. 2. Understand the basic notions particularly in parabolic geometry 3. Learn the examples to apply Cartan geometry to the classical problems in differential geometric structures.
Expected Learning Outcomes
- 1. Understand the basic notions in Cartan geometry. 2. Understand the basic notions particularly in parabolic geometry 3. Learn the examples to apply Cartan geometry to the classical problems in differential geometric structures.
Bibliography
Recommended Core Bibliography
- Differential Geometry : Cartan's Generalization of Klein's Erlangen Program, Foreword by S. S. Chern, Corrected 2nd printing, XIX, 421 p., Sharpe, R. W., 2000
Recommended Additional Bibliography
- Lie algebras and lie groups : 1964 lectures given at Harvard University, Serre, J.- P., 2006