MATHEMATICS (TURKISH, PHD) | |||||
PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 |
Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
MAT6024 | Advanced Differential Geometry II | Fall | 3 | 0 | 3 | 12 |
The course opens with the approval of the Department at the beginning of each semester |
Language of instruction: | Tr |
Type of course: | Departmental Elective |
Course Level: | |
Mode of Delivery: | Face to face |
Course Coordinator : | Prof. Dr. ERTUĞRUL ÖZDAMAR |
Course Objectives: | The object of the course is to provide basic concepts to students,of complex structures, holomorphic transformations, Hermitian and Kähler metrics, Riemannian manifolds and Kähler manifolds. |
The students who have succeeded in this course; The students who succeeded in this course; o will be able to know the concepts of complex structures and holomorphic maps and do basic calculations about them. o will be able to know Hodge and Dolbeault theories. o will be able to apply concepts of Complex and holomorphic vector bundles and Hermitian bundles o will be able to give examples of Kähler metrics o will be able to use natural operators on Riemannian and Kähler manifolds and the Ricci form of Kahler manifolds |
Complex structures and holomorphic maps Holomorphic forms and vector fields Complex and holomorphic vector bundles Hermitian bundles Hermitian and Kähler metrics The curvature tensor of Kähler manifolds Examples of Kähler metrics Natural operators on Riemannian and Kähler manifolds Hodge and Dolbeault theories The Ricci form of Kahler manifolds Kahler–Einstein metrics |
Week | Subject | Related Preparation | |
1) | Complex structures and holomorphic maps | ||
2) | Complex structures and holomorphic maps | ||
3) | Holomorphic forms and vector fields | ||
4) | Holomorphic forms and vector fields | ||
5) | Complex and holomorphic vector bundles | ||
6) | Complex and holomorphic vector bundles | ||
7) | Hermitian bundles | ||
8) | Hermitian and Kähler metrics | ||
9) | The curvature tensor of Kähler manifolds | ||
10) | Examples of Kähler metrics | ||
11) | Natural operators on Riemannian and Kähler manifolds | ||
12) | Hodge and Dolbeault theories | ||
13) | The Ricci form of Kahler manifolds | ||
14) | Kahler–Einstein metrics |
Course Notes: | Lectures on Kähler Geometry By Andrei Moroianu |
References: | . |
Semester Requirements | Number of Activities | Level of Contribution |
Attendance | 14 | % 10 |
Laboratory | % 0 | |
Application | % 0 | |
Field Work | % 0 | |
Special Course Internship (Work Placement) | % 0 | |
Quizzes | % 0 | |
Homework Assignments | 1 | % 10 |
Presentation | % 0 | |
Project | % 0 | |
Seminar | % 0 | |
Midterms | 1 | % 35 |
Preliminary Jury | % 0 | |
Final | 1 | % 45 |
Paper Submission | % 0 | |
Jury | % 0 | |
Bütünleme | % 0 | |
Total | % 100 | |
PERCENTAGE OF SEMESTER WORK | % 55 | |
PERCENTAGE OF FINAL WORK | % 45 | |
Total | % 100 |
Activities | Number of Activities | Duration (Hours) | Workload |
Course Hours | 14 | 3 | 42 |
Laboratory | 0 | 0 | 0 |
Application | 0 | 0 | 0 |
Special Course Internship (Work Placement) | 0 | 0 | 0 |
Field Work | 0 | 0 | 0 |
Study Hours Out of Class | 3 | 30 | 90 |
Presentations / Seminar | 0 | 0 | 0 |
Project | 0 | 0 | 0 |
Homework Assignments | 1 | 20 | 20 |
Quizzes | 0 | 0 | 0 |
Preliminary Jury | 0 | ||
Midterms | 1 | 20 | 20 |
Paper Submission | 0 | ||
Jury | 0 | ||
Final | 1 | 20 | 20 |
Total Workload | 192 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution |