Teaching
Advanced Topics in Differential Geometry: Symmetric spaces
References:
- Lecture 2 & 3: [Do] + Hatcher: Algebraic Topology
- Lecture 4 & 5: [Do, Ch. 5 & 7]
- Lecture 6 & 7 & 8: [Ma, Ch. 3 & 4.1]
- Lecture 9: [Le, Ex. 1.36]
- Lecture 10: [He, IV.2]
- Lecture 11: [He, IV.2; Le, Ch. 7.1, 20.1,20.2]
- Lecture 12: [He, Lem. 3.2]
- Lecture 13 & 14 & 15: [Sc, Ch.2; Le 20]
- Lecture 16 & 17 & 18: [He, Ch. II. 5 & 6]
- Lecture 19 & 20 & 21: [He, Ch. IV.3 & V.1]
- Lecture 22: [He, Ch. V. Prop. 4.2 & VIII.5]
- Lecture 23 & 24: [He, Ch. IV Thm. 4.2 Ch. V. 2 & 3; Pa, 4.1.3]
Notes: Lecture1, L2, L3, L4, L5, L6(new), L7(new), L8, L9, L10, L11, L12, L13, L14, L15, L16, L17, L18, L19, L20, L21, L22, L23, L24
Literature:
[He] Helgason: Differential Geometry, Lie groups and Symmetric Spaces.
[Ma] Maubon: Riemannian symmetric spaces of the non-compact type: differential geometry.
[Io] Iozzi: Symmetric spaces.
Further reading
[Ba] Ballmann: Symmetric spaces.
[Le] Lee: Introduction to smooth manifolds
[Pa] Paulin: Groupes et Geometries.
[Eb] Eberlein: Geometry of non positively curved manifolds.
[DC] Do Carmo: Riemannian geometry.
[BH] Bridson, Haefliger: Metric spaces of non-positive curvature.
[Ha] Hatcher: Algebraic topology.
[Sc] Schroeder: Symmetrische Räume.
[HI] Holland and Ion: Notes on symmetric spaces.
[Bo] Borel: Semisimple Groups and Riemannian Symmetric Spaces.
[KN] Kobayashi, Nomizu: Foundations of Differential Geometry vol. 1 and 2.
[Lo] Loos: Symmetric Spaces, vol. 1 and 2.
[Wo] Wolf: Spaces of constant curvature.
[Pa] Paradan: Symmetric spaces of the non-compact type: Lie groups.
Graduate Seminar on Differential Geometry: Spaces of non-positive curvature
Selected Topics in Geometry: An Introduction into higher rank Teichmüller theory.