| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Geometry of Submanifolds I | MAT548 | 3 + 0 | 3.0 | 8.0 |
| Prerequisites | None |
| Language of Instruction | Turkish |
| Course Level | Graduate |
| Course Type | |
| Mode of delivery | |
| Course Coordinator |
Res. Assist. Zehra İŞBİLİR |
| Instructors | |
| Assistants | |
| Goals | |
| Course Content | |
| Learning Outcomes |
- To examine submanifolds and teach basic equations. |
| Week | Topics | Learning Methods |
|---|---|---|
| 0. Week | Total geodesic submanifold | |
| 1. Week | Compact and oriented manifold | |
| 2. Week | Christoffel symbols, covariant derivative on submanifold | |
| 3. Week | Riemann-Christoffel curvature tensor | |
| 4. Week | Cross-sectional curvature | |
| 5. Week | Complete Riemannian manifold | |
| 6. Week | Conformal manifolds | |
| 7. Week | Isometric manifolds | |
| 8. Week | midterm | |
| 9. Week | space form | |
| 10. Week | Reduced connection in submanifolds | |
| 11. Week | Second Fundamental Form | |
| 12. Week | Normal bundle | |
| 13. Week | normal connection | |
| 14. Week | Total geodesic submanifold, Pseudo omblic submanifold |
| Bang-yen Chen, Geometry of Submanifolds, Marcel Dekker Inc., New York, 1973. Aminov, Yu. A. The Geometry of Submanifolds. Gordon and Breach Science Publishers, Singapore, 2001. |
| Program Requirements | Contribution Level | DK1 | Measurement Method |
|---|---|---|---|
| PY1 | 2 | 0 | - |
| PY2 | 2 | 0 | 60 |
| PY3 | 2 | 0 | 60 |
| PY4 | 2 | 0 | 60 |
| 0 | 1 | 2 | 3 | 4 | 5 | |
|---|---|---|---|---|---|---|
| Course's Level of contribution | None | Very Low | Low | Fair | High | Very High |
| Method of assessment/evaluation | Written exam | Oral Exams | Assignment/Project | Laboratory work | Presentation/Seminar |
| Event | Quantity | Duration (Hour) | Total Workload (Hour) |
|---|---|---|---|
| Midterm 1 | 1 | 2 | 2 |
| Midterm 2 | 1 | 2 | 2 |
| Homework 1 | 14 | 2 | 28 |
| Homework 2 | 14 | 2 | 28 |
| Quiz 1 | 14 | 1 | 14 |
| Quiz 2 | 14 | 1 | 14 |
| Final | 1 | 3 | 3 |
| Practice | 14 | 3 | 42 |
| Practice End-Of-Term | 14 | 3 | 42 |
| Classroom Activities | 14 | 2 | 28 |
| Total Workload | 203 | ||
| ECTS Credit of the Course | 8.0 | ||
