▶Japanese
Post to SNS
- Home
- > School of Science
- > Graduate major in Mathematics
- > Advanced topics in Geometry D
- School of Science
-
School of Engineering
- Undergraduate major in Mechanical Engineering
- Undergraduate major in Systems and Control Engineering
- Undergraduate major in Electrical and Electronic Engineering
- Undergraduate major in Information and Communications Engineering
- Undergraduate major in Industrial Engineering and Economics
- Common courses
- School of Materials and Chemical Technology
- School of Computing
- School of Life Science and Technology
- School of Environment and Society
- 工学院，物質理工学院，環境・社会理工学院共通科目
- Liberal arts and basic science courses
- First-Year Courses
- School of Science
- School of Engineering
- School of Materials and Chemical Technology
- School of Computing
- School of Life Science and Technology
-
School of Environment and Society
- Department of Architecture and Building Engineering
- Department of Civil and Environmental Engineering
- Department of Transdisciplinary Science and Engineering
- Department of Social and Human Sciences
- Department of Innovation Science
- Graduate major in Technology and Innovation Management
- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Hattori Toshiaki
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Mon3-4(H115)
- Group
- -
- Course number
- MTH.B404
- Credits
- 1
- Academic year
- 2018
- Offered quarter
- 4Q
- Syllabus updated
- 2018/3/20
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
The aim of this lecture is to familiarize the students with the basic l
anguage of and some fundamental theorems in Riemannian geometry.
This course is a continuation of [MTH.B403 : Advanced topics in Geometry C].
Student learning outcomes
Students are expected to
・understand the definition of geodesic and the theorem on completeness.
・understand that Einstein equation is a second order non-linear partial differential equation for Riemannian metrics.
Keywords
Parallel translation, geodesic, exponential map, normal cocordinate neighborhood, Einstein equation, Hopf-Rinow Theorem
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
Standard lecture course
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Parallel translation | Details will be provided during each class session |
| Class 2 | The definitions of geodesics and the equations of geodesics | Details will be provided during each class session |
| Class 3 | Exponential map | Details will be provided during each class session |
| Class 4 | Normal coordinate neighborhood, Gauss' lemma | Details will be provided during each class session |
| Class 5 | Geodesics are locally minimizing curves | Details will be provided during each class session |
| Class 6 | Einstein equation and Hopf-Rinow theorem | Details will be provided during each class session |
| Class 7 | Proof of Hopf-Rinow theorem | Details will be provided during each class session |
| Class 8 | Jacobi field | Details will be provided during each class session |
Textbook(s)
Non required
Reference books, course materials, etc.
M.do Carmo, Riemannian Geometry, Birkhauser
S. Gallot, D. Hulin and J. Lafontaine, Riemannian Geometry, Springer
Assessment criteria and methods
Exams and reports. Details will be provided during class sessions.
Related courses
- MTH.B301 ： Geometry I
- MTH.B302 ： Geometry II
- MTH.B331 ： Geometry III
- MTH.B403 ： Advanced topics in Geometry C
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Students are expected to have passed [Advanced topics in Geometry C]
