BAHÇEŞEHİR UNIVERSITY BİLGİ PAKETİ / DERS KATALOĞU
| MATHEMATICS (TURKISH, PHD) | |||||
| PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 | ||
Course Introduction and Application Information
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT6024 | Advanced Differential Geometry II | Fall Spring |
3 | 0 | 3 | 8 |
| This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
Basic information
| Language of instruction: | Turkish |
| Type of course: | Departmental Elective |
| Course Level: | |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Prof. Dr. ERTUĞRUL ÖZDAMAR |
| Recommended Optional Program Components: | None |
| 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. |
Learning Outcomes
|
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 |
Course Content
| 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 |
Weekly Detailed Course Contents
| 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 |
Sources
| Course Notes / Textbooks: | Lectures on Kähler Geometry By Andrei Moroianu |
| References: | . |
Evaluation System
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | 14 | % 10 |
| Homework Assignments | 1 | % 10 |
| Midterms | 1 | % 35 |
| Final | 1 | % 45 |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 55 | |
| PERCENTAGE OF FINAL WORK | % 45 | |
| Total | % 100 | |
ECTS / Workload Table
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Study Hours Out of Class | 3 | 30 | 90 |
| Homework Assignments | 1 | 20 | 20 |
| Midterms | 1 | 20 | 20 |
| Final | 1 | 20 | 20 |
| Total Workload | 192 | ||
Contribution of Learning Outcomes to Programme Outcomes
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |