Course title
6M0052001
Advanced Differential Geometry

 suzuki tatsuo Click to show questionnaire result at 2018
Course content
Differential geometry is a mathematical discipline that uses the techniques of differential calculus and integral calculus to study problems in geometry. This course aims to learn about Riemannian manifolds, complex manifolds, their connections and curvatures. The course will also introduce some applications.
Purpose of class
The object of this course is to understand fundamental concepts of Riemannian manifolds and to be able to calculate some connections and there curvatures.
Goals and objectives
  1. To understand fundamental concepts of manifolds
  2. To understand fundamental concepts of Riemannian manifolds
  3. To be able to calculate some connections and there curvatures
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1． Geometry of Euclid plane Review of manifolds 150minutes
2． Differentiable manifolds Review of Geometry of Euclid plane 200minutes
3． Tangent space, cotangent space Review of Differentiable manifolds 200minutes
4． Vector fields Review of Tangent space, cotangent space 200minutes
5． Differential forms Review of Vector fields 200minutes
6． Tensor fields Review of Differential forms 200minutes
7． Riemannian metrics Review of Tensor fields 200minutes
8． Riemannian manifolds Review of Riemannian metrics 200minutes
9． Covariant derivative of vector fields Review of Riemannian manifolds 200minutes
10． Affine connection, Levi-Civita connection Review of Covariant derivative of vector fields 200minutes
11． Geodesics Review of Affine connection, Levi-Civita connection 200minutes
12． Curvature tensor fields Review of Geodesics 200minutes
13． Information geometry Review of Curvature tensor fields 200minutes
14． Physics and differential geometry Review of the above 200minutes
Total. - - 2750minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 report1 report2 Total.
1. 20% 20% 40%
2. 20% 20% 40%
3. 0% 20% 20%
Total. 40% 60% -
Evaluation method and criteria
report: 100%
Textbooks and reference materials
Handouts will be provided.
Prerequisites
Topology, group theory, manifold theory.
Office hours and How to contact professors for questions
  • Before or after class
Relation to the environment
Non-environment-related course
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Non-social and professional independence development course
Active-learning course
More than one class is interactive
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicatable
N/A N/A
Last modified : Thu Mar 21 15:30:25 JST 2019