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． Differential Geometry and sets of matrices Review of manifolds 150minutes
2． Differentiable manifolds Review of Differential Geometry and sets of matrices 200minutes
3． Riemannian metrics Review of Differentiable manifolds 200minutes
4． Examples of Riemannian metrics Review of Riemannian metrics 200minutes
5． Covariant derivative of vector fields, Affine connection Review of Examples of Riemannian metrics 200minutes
6． Curvature tensor fields Review of Covariant derivative of vector fields, Affine connection 200minutes
7． Some calculations of curvatures and assignment Review of Curvature tensor fields 200minutes
8． Geodesics Review of Affine connection 200minutes
9． Examples of geodesics Review of Geodesics 200minutes
10． Information geometry Review of Examples of geodesics 200minutes
11． Dual affine connections Review of Information geometry 200minutes
12． Divergences Review of Dual affine connections 200minutes
13． Generalized Pythagorean theorem Review of Divergences 200minutes
14． Presentation and its commentary Review of the above 200minutes
Total. - - 2750minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Assignment Presentation Total.
1. 20% 20% 40%
2. 20% 20% 40%
3. 10% 10% 20%
Total. 50% 50% -
Evaluation method and criteria
Assignment (50%), Presentation(50%)
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 : Wed Mar 23 04:23:15 JST 2022