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- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Yamada Kotaro
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- Day/Period(Room No.)
- Tue3-4(M-B107(H104))
- Group
- -
- Course number
- MTH.B505
- Credits
- 1
- Academic year
- 2023
- Offered quarter
- 1Q
- Syllabus updated
- 2023/3/20
- Lecture notes updated
- -
- Language used
- English
- Access Index
-
Course description and aims
As an informal introduction to Riemannian manifold, geometry of submanifolds in (pseudo) Euclidean
spaces is introduced.
Student learning outcomes
Students are expected to learn
- Pseudo Euclidean space.
- Induced metrics on submanifolds in a (pseudo) Euclidean space.
- Covariant derivatives on submanifolds.
- Geodesics on submanifolds.
Keywords
pseudo Euclidean space, submanifolds, Riemannian connections, geodesics
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
A standard lecture course.
Homeworks will be assined for each lesson.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Bilinear forms | Details will be provided during each class session. |
| Class 2 | Pseudo Euclidean spaces | Details will be provided during each class session. |
| Class 3 | Submanifolds and induced metrics | Details will be provided during each class session. |
| Class 4 | Differential forms | Details will be provided during each class session. |
| Class 5 | The Riemannian connection | Details will be provided during each class session. |
| Class 6 | Geodesics | Details will be provided during each class session. |
| Class 7 | Hopf-Rinow's theorem | Details will be provided during each class session. |
Out-of-Class Study Time (Preparation and Review)
Formal Message: To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and
another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
No textbook is set. Lecture note will be provided.
Reference books, course materials, etc.
Masaaki Umehara and Kotaro Yamada, Differential Geometry of Curves and Surfaces, Transl. by Wayne Rossman, World Scientific Publ.,
2017, ISBN 978-9814740234 (hardcover); 978-9814740241 (softcover)
Loring W. Tu, Differential Geometry,Graduate Texts in Mathematics, Springer-Verlag, 2017, ISBN 978-3-319-55082-4, 978-3-319-55084-8 (eBook)
Assessment criteria and methods
Graded by homeworks. Details will be announced through T2SCHOLA
Related courses
- MTH.B506 ： Advanced topics in Geometry F1
Prerequisites (i.e., required knowledge, skills, courses, etc.)
At least, knowledge of undergraduate calculus and linear algebra are required.
Contact information (e-mail and phone) Notice : Please replace from "[at]" to "@"(half-width character).
kotaro[at]math.titech.ac.jp
Office hours
N/A
Other
Web page:
http://www.math.titech.ac.jp/~kotaro/class/2023/geom-e1
http://www.official.kotaroy.com/class/2023/geom-e1
