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- Academic unit or major
- Mathematics
- Instructor(s)
- Yamada Kotaro
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Tue3-4(H104)
- Group
- -
- Course number
- ZUA.B331
- Credits
- 1
- Academic year
- 2019
- Offered quarter
- 1Q
- Syllabus updated
- 2019/3/18
- 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, covariant derivatives.
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 | Metric vector spaces | Details will be provided during each class session |
| Class 3 | Pseudo Euclidean space | Details will be provided during each class session |
| Class 4 | Induced metrics on submanifolds | Details will be provided during each class session |
| Class 5 | Vector fields on submanifolds | Details will be provided during each class session |
| Class 6 | Covariant derivatives | Details will be provided during each class session |
| Class 7 | Geodesics and completeness | Details will be provided during each class session |
Textbook(s)
No textbook is set.
Lecture note will be provided.
Reference books, course materials, etc.
B. O'Neill, Semi-Riemannian Geometry, Academic Press, 1983; ISBN-13: 978-0-12-526740-3
Assessment criteria and methods
Graded by homeworks
Related courses
- MTH.B211 ： Introduction to Geometry I
- MTH.B212 ： Introduction to Geometry II
- MTH.B301 ： Geometry I
- MTH.B302 ： Geometry II
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Knowledge on differential geometry of curves and surfaces (as in MTH.B211 "Introduction to Geometry I" and MTH.B212 "Introduction to Geometry II", or Sections 1 to 10 of the text book "Differential Geometry of Curves and Surfaces" by M. Umehara and K.
Yamada), and knowledge of fundamental notions of differentiable manifolds (MTH.301/MTH.302) 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. Contact by E-mails, or at the classroom.
Other
For details, visit the web-site of this class http://www.math.titech.ac.jp/~kotaro/class/2019/geom-a
