Special Mathematics Lecture
Serge Richard (email@example.com), Rm. 237 in Sci. Bldg. A
Differential geometry (Fall 2018)
Registration code : 0063611
Schedule : Wednesday (18:30 - 20.00) in room 207 of the Science Building A
Registration: See page 15 of
Additional support for Japanese students:
Class dates :
October 3, 10, 17, 24, 31
November 7, 14, 21, 28
December 12, 19
January 9, 16, 23
I) Differentiable manifolds:
II) Tensors, tensor fields and differential forms:
III) Integration on manifolds:
IV) Riemannian manifolds:
VI) General relativity
Study sessions /
trailer for prospective Japanese students
Thursday at 6.30 in room 207 of Science Building A, with
Monday at 6.30 in room 207 of Science Building A, with
Tuesday at 6.30 in room 207 of Science Building A, with
Song Ha and
The cumulative notes :
Notes taken by Liyang Zhang, with the table of content and the appendices:
(this file is 35 MB)
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, please contact me
or Syoji Toyota.
Works submitted by the students :
Examples of smooth manifolds, by Liyang Zhang
A homomorphism between tangent spaces, by Bui Dang Cong and Arata Suzuki
Homomorphisms of vector space and algebra, Song Ha Nguyen, Yuki Katsurada, and Duc Truyen Dam
On the dual of a vector space, by Koichi Kato
On the dual of a vector space, by Yoshiyuki Endo
On two definitions of continuity, by Yoshiyuki Endo
A tangent vector in 2 coordinate systems, by Liyang Zhang
On the dual of a vector space, by Shihab Fadda
On the dual of a vector space, Song Ha Nguyen, Arata Suzuki, and Duc Truyen Dam
Equivalence of 2 definitions of continuity, by Tomoya Tatsuno
Commutators of vector fields, by Sparsh Mishra
On the wedge product, Song Ha Nguyen, Arata Suzuki, and Bui Dang Cong
On curvature and torsion, by Liyang Zhang, Chang Sun, Tomoya Tatsuno, Arata Suzuki, Koichi Kato
On curvature and torsion, by Sparsh Mishra
On de Rham cohomology, by Takuya Ishibashi
On the Lie algebra of smooth vector fields, by Yuki Katsurada and Arata Suzuki
Tensors, Duc Truyen Dam
On curvature for torsion free connection, by Yuki Katsurada, Arata Suzuki,
Song Ha Nguyen, Bui Dang Cong and Duc Truyen Dam
On affine connection, by Sparsh Mishra
An example of a topological manifold: the torus, by Yoshiyuki Endo
On some properties of the curvature tensor, by Chang Sun
Uniqueness of the maximal atlas, by Saki Takamatsu
About the existence of a partition of unity, by Yoshihiko Terasawa
The tangent bundle, by Naohiro Tsuzu
On two definitions of continuity, and on commutator properties, by Kai Levi Turner
On two homomorphisms, by Mao Fujiwara
About tangent space, Lie Bracket, and alternating tensors, by Quang Nhat Nguyen
On two homomorphisms, by James Boyle
Riemannian metrics and immersion, by James Boyle
Properties of tensors, by James Boyle
On sectional curvatures, by Shihab Fadda
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
Pictures taken in November :
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