講義名 幾何学特論B1（Advanced topics in Geometry B1）　　科目コード：MTH.B406
開講学期 ２Q 単位数 1--0--0
担当 山田　光太郎　教授：本館２階２３１号室（内線３３８９）

【講義の概要とねらい】
As an application of the fundamental theorem for surface theory, construction of pseudospherical surfaces, which are local models of Lobachevsky's non-euclidean geometry, will be introduced.

【到達目標】
Students will learn a way to apply the fundamental theorem for surface theory, and observe various mathematical phenomena in the way of construction.

【キーワード】
Fundamental theorem of surface theory, pseudospherical surfaces, sine Gordon equations

【学生が身につける力】
Specialist skills

【授業の進め方】
A standard lecture course

【授業計画・課題】

Class 1	Non-euclidean geometry
Class 2	Surfaces of constant Gaussian curvature
Class 3	Pseudospherical surfaces and asymptotic Chebyshev net
Class 4	A construction of pseudospherical surfaces
Class 5	Hilbert's theorem
Class 6	Surfaces in Lorentz-Minkowski space
Class 7	Realization of the hyperbolic plane

Details will be provided during each class session

【授業時間外学修（予習・復習等）】
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 LMS (formerly T2SCHOLA)

【関連する科目】
MTH.B211 ： Introduction to Geometry I
MTH.B212 ： Introduction to Geometry II

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

【その他】
Visit http://www.kotaroy.com/official/class/2025-geom-b1 for details