Special Mathematics Lecture

Contact:
Serge Richard (richard@math.nagoya-u.ac.jp), Rm. 247 in Sci. Bldg. A

Differential geometry (Fall 2024)

Registration code : 0063611
Schedule : Wednesday (18.30 - 20.00) in room 207 of Science building A and on Zoom

• Syllabus : see here

• SML official rule : See here

• NU EMI : Link to the website

• PRESS : One article in the Chunichi Shimbun related to NUEMI and this course, and its translation in The Japan Times

• Class dates :
  October 2, 9, 16, 23, 30
  November 6, 13, 20, 27
  December 4, 11, 18, 25
  January 8, 15
  

• Program (tentative) :
  I) Differentiable manifolds
  II) Tensors, tensor fields and differential forms
  III) Integration on manifolds
  IV) Riemannian manifolds
  V) Curvature
  VI) General relativity
  

• Lecture notes : (updated on a regular basis)
  The cumulative notes

• Weekly summaries and summary : 1, 2, 3, 4, 5, 6, Summary, 7, 8,

• Study sessions : Will be organized on an individual basis by some students.

• For the evaluation, you need to submit the solutions of some exercises and/or the proofs of some statements. These submissions can take place at any time during the semester. If you have any question, contact me or Fujii Moe.

• Works submitted by the students :
  Homomorphisms of algebras and tangent spaces, by Rafi Rizqy Firdaus
  Topological spaces and Hausdorff property, by Yamamoto Mei
  Homomorphisms of algebras and tangent spaces, by Koichi Kato
  Proving that ℝⁿ is a topological manifold, by Hadiko Rifqi Aufa Sholih
  Topological spaces, by Elisabeth Bérat
  Topological spaces and topological manifolds, by Théo Lesieur
  Hausdorff property and subspace topology, by Elisabeth Bérat
  On the dual of a finite dimensional real vector space, by Koichi Kato
  Antisymmetry, wedge product, and exterior algebra, by Luk Yat Ming
  

• References : (electronic version available upon request)
  [Au] A course in differential geometry, written by T. Aubin. Slightly more difficult, but still short
  [Be] Einstein manifolds, written by A. L. Besse. Extensive chapter 10 on holonomy groups
  [Bo] An introduction to differentiable manifolds and Riemannian geometry, written by W. M. Boothby. Slightly more involved but beautifully written
  [CS] Holonomy groups in Riemannian geometry, written by A. Clarke and B. Santoro. Lecture notes centred on holonomy groups
  [GN] An Introduction to Riemannian Geometry, written by L. Godinho and J. Natario. Certainly the main reference for this course
  [Kl] A course in differential geometry, written by W. Klingenberg. A pedestrian introduction to differential geometry, focussing on low dimensions
  [Pe] The Whitney embedding theorem, written by M. Persson. Looks very good for a graduation thesis
  [St] General relativity, written by N. Straumann. A classic book about general relativity
  [Th] Elementary topics in differential geometry, written by J. A. Thorpe. An accessible introduction to extrinsic differential geometry
  [Tu1] An Introduction to manifolds, written by L. W. Tu. Another excellent reference with useful appendices
  [Tu2] Differential geometry, written by L. W. Tu. Another excellent reference, more advanced