講義名 幾何学特論F（Advanced topics in Geometry F） 科目コード：MTH.B502
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】
A local theory of Riemannian manifolds and fundamental theorem of
surface theory for surface in Riemannian 3-manifolds of constant
scetional curvature are introduced. As an application, a relationship of
surfaces of constant mean curvature surface in different spaces,
e.g. minimal surfaces in Euclidean 3-space and constant curvature one surfaces in hyperbolic space, is discussed.
【到達目標】
Students will learn: a local theory of Riemannian manifolds, i.e.
notions of Riemannian metrics, sectional curvatures; spaces of constant
curvature (space forms); an extension of the fundamental theorem of
surface theory for surfaces in 3-dimensional space forms.
【キーワード】
Riemannian metric, curvature, space form, fundamental theorem of surface theory
【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 | Riemannian metrics and connections |
| 第2回 | Curvatures |
| 第3回 | Euclidean spaces and Spheres |
| 第4回 | Lorentz-Minkowski space |
| 第5回 | Hyperbolic spaces |
| 第6回 | Fundamental theorem of surface theory revisited |
| 第7回 | Constant mean curvature surfaces in 3-dimensional space forms |
課題は講義中に指示する
【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 T2SCHOLA.
【関連する科目】
MTH.B301 ： 幾何学第一
MTH.B302 ： 幾何学第二
MTH.B501 ： 幾何学特論E
【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.
Attending the class "Advanced Topics in Geometry E" (MTH.B501) is strongly recommended.
【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-f for details.