Course title
6M0052001
Advanced Differential Geometry

 suzuki tatsuo Click to show questionnaire result at 2019
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 be able to construct an atlas of sphere
  2. To be able to show some examples of Riemannian manifolds and their metrics
  3. To be able to calculate Christoffel symbols and there curvatures from a Riemannian metric
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, Lie groups Review of Geometry of Euclid plane 200minutes
3． Tangent space, vector fields Review of Differentiable manifolds 200minutes
4． Lie algebras Review of Lie groups 200minutes
5． Homogeneous spaces Review of Lie groups and Lie algebras 200minutes
6． Tensor fields, Riemannian metrics Review of Differentiable manifolds 200minutes
7． Complex projective spaces Review of Differentiable manifolds and Riemannian metrics 200minutes
8． Covariant derivative of vector fields, Affine connection Review of Riemannian metrics 200minutes
9． Geodesics Review of Affine connection 200minutes
10． Curvature tensor fields Review of Covariant derivative of vector fields, Affine connection 200minutes
11． Information geometry Review of normal distributions 200minutes
12． Dual affine connections Review of Affine connection, Information geometry 200minutes
13． Divergences Review of Dual affine connections 200minutes
14． Generalized Pythagorean theorem Review of Divergences 200minutes
Total. - - 2750minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Assignment 1 Assignment 2 Total.
1. 20% 20% 40%
2. 20% 20% 40%
3. 0% 20% 20%
Total. 40% 60% -
Evaluation method and criteria
Assignment 1 (40%), assignment 2 (60%)
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
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 applicable
N/A N/A
Education related SDGs:the Sustainable Development Goals
  • 4.QUALITY EDUCATION
Last modified : Sun Mar 28 04:05:09 JST 2021