2026/2027

Introduction to Finsler Geometry

Type: Optional course (faculty)

Delivered by: Faculty of Mathematics

Where: Faculty of Mathematics

When: 3, 4 module

Open to: students of all HSE University campuses

Instructors: Tianyu Ma

Language: English

ECTS credits: 6

Contact hours: 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.