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- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Yamada Kotaro
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Tue3-4(H104)
- Group
- -
- Course number
- MTH.B402
- Credits
- 1
- Academic year
- 2018
- Offered quarter
- 2Q
- Syllabus updated
- 2018/3/20
- Lecture notes updated
- 2018/7/3
- Language used
- Japanese
- Access Index
-
Course description and aims
As a continuation of theory for surfaces in Euclidean space, the fundamentall theorem for surface theory and its applications, including a construction of constant mean curvature tori, are explained.
Student learning outcomes
Students are expected to learn
- the fundamental theorem for surface theory,
- and an outline of construction of constant mean curvature tori.
Keywords
The fundamental theorem for surface theory, Hopf's theorem, constant mean curvature tori
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 | Linear ordinary differential equations | Details will be provided during each class session |
| Class 2 | Integrability conditions for systems of linear partial differential equations | Details will be provided during each class session |
| Class 3 | The fundamental theorem for surface theory | Details will be provided during each class session |
| Class 4 | Isothermal parameters and curvature line parameters | Details will be provided during each class session |
| Class 5 | Hopf's theorem | Details will be provided during each class session |
| Class 6 | A construction of constant mean curvature tori | Details will be provided during each class session |
| Class 7 | Principal curvature lines of constant mean curvature tori | Details will be provided during each class session |
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)
Katsuei Kenmotsu, Surfaces with constant mean curvature, Transl. by Katsuhiro Moriya, Translations of Mathematical Monographs, American Mathematical Society, 2003, ISBN 978-0821834794
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 differentable 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/2018/geom-b
