2026/2027

Введение в финслерову геометрию

Статус: Дисциплина общефакультетского пула

Кто читает: Факультет математики

Где читается: Факультет математики

Когда читается: 3, 4 модуль

Охват аудитории: для всех кампусов НИУ ВШЭ

Преподаватели: Ма Тяньюй

Язык: английский

Кредиты: 6

Контактные часы: 72

Course Syllabus

Abstract

Finsler geometry is the natural generalization of Riemannian geometry, with the inner products on the tangent spaces replaced by norm functions. This generalization enables rich freedom in both the geometric structures themselves and also the objects that admit such mathematical models. In this course, we will study the basic notions and properties of Finsler manifolds, in comparison with Riemannian geometry. Topics in this course include the Finslerian version of various connections and curvatures, Gauss-Bonnet, Hopf-Rinow theorem, cut/conjugate loci, comparison theorems, constant-curvature and special Finsler spaces, among other topics. Elementary knowledge of differential geometry is assumed as a prerequisite for this course.