Interactive Syllabus

Elements of Finsler Geometry and its Applications

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I shall display the individual recordings of the lectures here.

Lecture 1. Motivation, Minkowski norms, Finsler metrics, examples (in particular Randers metrics)

Lecture 2. Cartan torsion and mean torsion, characterization of Riemannian and Randers metrics, Chern's structure equations

Lecture 3. Horizontal splitting of the second tangent bundle, sprays, Finsler geodesics

Lecture 4. Towards some applications (lecture by Temesgen)

Lecture 5. Curvature

Lecture 6. The Finsler co-norms and the Hamiltonian approach. Unfortunately, I missed hitting the recording key in the 6th lecture. I attach at least the pictures of the two boards:

The Hamiltonian point of view - Board 1

The Hamiltonian point of view - Board 2

Lecture 7. The geometry of sprays.

2nd order ODES, sprays, projective equivalence, curvatures, etc.

and the two boards:

first board

second board

Two papers behind the 7th and 8th lectures:

DGA12 Crampin Mestdag Saunders 1 s2.0 S092622451200099X main

DGA13 Crampin Mestdag Saunders 1 s2.0 S092622451200099X main

Lecture 8. Finsler metrizability of projective classes of sprays

Path geometries, projective classes of sprays, metrizability

first board

second board

Lecture 9. Computation of Finsler Geometry objects in Maple

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Elements of Finsler Geometry and its Applications

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