As a continuation of theory for surfaces in Euclidean space, the fundamental theorem for surface theory and its applications, including a construction of constant mean curvature tori, are explained.
Students are expected to learn
- the fundamental theorem for surface theory,
- and an outline of construction of constant mean curvature tori.
The fundamental theorem for surface theory, Hopf's theorem, constant mean curvature tori
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
A standard lecture course.
Homeworks will be assigned for each lesson.
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 |
No textbook is set.
Lecture note will be provided.
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
Graded by homeworks
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 space forms (e.g. ZUA.B331) are required.
kotaro[at]math.titech.ac.jp
N/A. Contact by E-mails, or at the classroom.
For details, visit the web-site of this class http://www.math.titech.ac.jp/~kotaro/class/2018/geom-b