Магистратура
2025/2026
Введение в дифференциальную геометрию
Статус:
Курс по выбору (Математика)
Кто читает:
Факультет математики
Где читается:
Факультет математики
Когда читается:
1-й курс, 1, 2 модуль
Охват аудитории:
для своего кампуса
Преподаватели:
Уваров Филипп Викторович
Язык:
английский
Кредиты:
6
Course Syllabus
Abstract
The course serves as an introduction to the main topics of Differential geometry: an initial introduction to symplectic and contact geometry, the theory of affine connections on manifolds, Riemannian manifolds, geodesics. PRELIMINARY PREPARATION: Linear algebra, differential equations, analysis on manifolds
Learning Objectives
- In this course you will learn the basic tools of differential geometry. The main subjects of study will be differential forms on manifolds, Riemannian metrics, vector and principal bundles, connections, curvatures, characteristic classes, complex and almost complex structures.
Expected Learning Outcomes
- Learn smooth manifolds
- Learn differential forms
- Learn Riemannian metric
- Learn vector bundles
- Learn curvature
- Learn curvarure
- Learn covariant derivatives
- Learn complex varieties
Course Contents
- Smooth manifolds
- Differential forms on manifolds.
- Riemannian metric on a manifold, geodesics, Hodge’s operator
- Vector bundles and principal bundles on manifolds
- Connections on principal and vector bundles, covariant differentiation
- Connectivity curvature. Characteristic classes
- Covariant derivatives and metrics. Riemannian curvature tensor.
- Complex and almost complex varieties
Interim Assessment
- 2025/2026 2nd module0.25 * Презентация задач на семинарах + 0.25 * Презентация задач на семинарах + 0.5 * Экзамен
