Advanced Differential Geometry II
Mathematics
Institute of Natural and Applied Sciences
Second Cycle (Master's Degree)
| Course Unit Title | Course Unit Code | Type of Course Unit | Level of Course Unit | Year of Study | Semester | ECTS Credits |
|---|---|---|---|---|---|---|
| Advanced Differential Geometry II | MAT516 | Elective | Master's degree | 1 | Spring | 8 |
Name of Lecturer(s)
Associate Prof. Dr. İlim KİŞİ
Associate Prof. Dr. Günay ÖZTÜRK
Assistant Prof. Dr. Ahmet ZOR
Research Assistant Nizamettin Ufuk BOSTAN
Learning Outcomes of the Course Unit
1) Recognize the Levi-Civita connection.
2) Explain the isometries.
3) Apply the parallel transport.
4) Recognize the structure of geodesics.
5) Recognize Riemannian curvature and sectional curvature.
6) Recognize the Ricci curvature and skalar curvature.
7) Explain the product manifolds.
Program Competencies-Learning Outcomes Relation
| Program Competencies | ||||||||
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | ||
| Learning Outcomes | ||||||||
| 1 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 2 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 3 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 4 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 5 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 6 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 7 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
Mode of Delivery
Face to Face
Prerequisites and Co-Requisites
None
Recommended Optional Programme Components
Diferensiyel Geometri 1,2
Course Contents
This course provides candidates with profound knowledge on symmetric bilinear forms, skalar products. isometries, Levi-Civita connection, parallel translation, godesics, the exponential map, curvature. sectional curvature, semi-Riemannian surfaces, frame fields, some differential operators, Ricci and Scalar Curvature, semi-Riemannian product manifolds and local isometries.
Weekly Schedule
1) symmetric bilinear forms2) skalar products
3) isometries
4) Levi-Civita connection
5) parallel translation
6) godesics
7) the exponential map, curvature. sectional curvature
8) midterm
9) semi-Riemannian surfaces, frame fields
10) some differential operators
11) Ricci and Scalar Curvature
12) semi-Riemannian product manifolds
13) local isometries
14) local isometries
15) general again.
16) general again and question solution
Recommended or Required Reading
Planned Learning Activities and Teaching Methods
1) Lecture
2) Lecture
3) Question-Answer
4) Question-Answer
5) Discussion
6) Drill and Practice
7) Drill and Practice
8) Brain Storming
9) Brain Storming
10) Self Study
11) Self Study
12) Problem Solving
13) Problem Solving
Assessment Methods and Criteria
Contribution of Midterm Examination to Course Grade |
40% |
|---|---|
Contribution of Final Examination to Course Grade |
60% |
Total |
100% |
Language of Instruction
Turkish
Work Placement(s)
Not Required