2019 Advanced topics in Geometry A1

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Academic unit or major
Graduate major in Mathematics
Instructor(s)
Yamada Kotaro 
Course component(s)
Lecture
Day/Period(Room No.)
Tue3-4(H104)  
Group
-
Course number
MTH.B405
Credits
1
Academic year
2019
Offered quarter
1Q
Syllabus updated
2019/3/18
Lecture notes updated
2019/7/21
Language used
English
Access Index

Course description and aims

As an informal introduction to Riemannian manifold, geometry of submanifolds in (pseudo) Euclidean spaces is introduced.

Student learning outcomes

Students are expected to learn
- Pseudo Euclidean space.
- Induced metrics on submanifolds in a (pseudo) Euclidean space.
- Covariant derivatives on submanifolds.
- Geodesics on submanifolds.

Keywords

pseudo Euclidean space, submanifolds, covariant derivatives.

Competencies that will be developed

Intercultural skills Communication skills Specialist skills Critical thinking skills Practical and/or problem-solving skills
- - - -

Class flow

A standard lecture course.
Homeworks will be assined for each lesson.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Bilinear forms Details will be provided during each class session
Class 2 Metric vector spaces Details will be provided during each class session
Class 3 Pseudo Euclidean space Details will be provided during each class session
Class 4 Induced metrics on submanifolds Details will be provided during each class session
Class 5 Vector fields on submanifolds Details will be provided during each class session
Class 6 Covariant derivatives Details will be provided during each class session
Class 7 Geodesics and completeness Details will be provided during each class session

Textbook(s)

No textbook is set.
Lecture note will be provided.

Reference books, course materials, etc.

B. O'Neill, Semi-Riemannian Geometry, Academic Press, 1983; ISBN-13: 978-0-12-526740-3

Assessment criteria and methods

Graded by homeworks

Related courses

  • MTH.B211 : Introduction to Geometry I
  • MTH.B212 : Introduction to Geometry II
  • MTH.B211 : Introduction to Geometry I
  • MTH.B212 : Introduction to Geometry II

Prerequisites (i.e., required knowledge, skills, courses, etc.)

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 differentable manifolds (MTH.301/MTH.302) are required.

Contact information (e-mail and phone)    Notice : Please replace from "[at]" to "@"(half-width character).

kotaro[at]math.titechac.jp

Office hours

N/A. Contact by E-mails, or at the classroom.

Other

For details, visit the web-site of this class http://www.math.titech.ac.jp/~kotaro/class/2019/geom-a

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