幾何学特論E

【講義の概要とねらい】

The fundamental theorem of surface theory and its applications will be introduced.

【到達目標】
Students will learn the fundamental theorem of surface theory and its peripheral matters, including a theory of surfaces of constant negative curvature.

【キーワード】
the fundamental theorem of surface theory, integrability conditions

【学生が身につける力】
Specialist skills

【授業の進め方】
A standard lecture course. Homeworks will be assined for each lesson.

【授業計画・課題】

第1回	Linear ordinary differential equations
第2回	Integrability conditions
第3回	Review of surface theory
第4回	Gauss and Codazzi equations
第5回	Fundamental theorem for surface theory
第6回	Asymptotic Chebyshev net and the sine-Gordon equation
第7回	Bäcklund transformations

Details will be provided during each class session.

【Out-of-Class Study Time (Preparation and Review) 】
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.

【教科書】
No textbook is set. Lecture note will be provided.

【参考書、講義資料等】
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)

【成績評価の基準及び方法】
Graded by homeworks. Details will be announced through T2SCHOLA

【関連する科目】
MTH.B211 ：幾何学概論第一
MTH.B212 ：幾何学概論第二

【履修の条件（知識・技能・履修科目等）】
At least, knowledge of undergraduate calculus and linear algebra are required.

【連絡先（メール、電話番号）】 　※”[at]”を”@”(半角)に変換してください。
kotaro[at]math.titech.ac.jp

【オフィスアワー】
N/A

【その他】
Visit http://www.math.titech.ac.jp/~kotaro/class/2022/geom-e for details.