The fundamental theorem of surface theory and its applications will be introduced.
Students will learn the fundamental theorem of surface theory and its peripheral matters, including a theory of surfaces of constant negative curvature.
the fundamental theorem of surface theory, integrability conditions
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
A standard lecture course. Homeworks will be assined 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 | Details will be provided during each class session. |
Class 3 | Review of surface theory | Details will be provided during each class session. |
Class 4 | Gauss and Codazzi equations | Details will be provided during each class session. |
Class 5 | Fundamental theorem for surface theory | Details will be provided during each class session. |
Class 6 | Asymptotic Chebyshev net and the sine-Gordon equation | Details will be provided during each class session. |
Class 7 | Bäcklund transformations | Details will be provided during each class session. |
Official 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.
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)
Graded by homeworks. Details will be announced through T2SCHOLA
At least, knowledge of undergraduate calculus and linear algebra are required.
kotaro[at]math.titech.ac.jp
N/A
Visit http://www.math.titech.ac.jp/~kotaro/class/2022/geom-e for details.