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 |
| MAT6027 | Semi-Riemannian Geometry | Fall | 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: | |
| Course Coordinator : | Prof. Dr. ERTUĞRUL ÖZDAMAR |
| Recommended Optional Program Components: | None |
| Course Objectives: | Yari-Riemann geometrisi dersi, Lorentz ve genelde de Yari-Riemann geometriye bir giriş dersidir. During the course, basic information aimed to meet the needs of researchers. |
Learning Outcomes
|
The students who have succeeded in this course; upon succeeding this course the student will be able to 1) know the concepts of manifold and the curvature tensor, and understood very well the role of the inner-dot product, 2) calculate the distance, area and curvature on Semi-Riemannian manifolds. 3) explain the properties of geodesics on Semi-Riemannian manifolds, and also the concepts as chronology and time cone 4) understand paradoxes in relativity. 5) Explain all properties of Warped product and the metric matrices. |
Course Content
| Manifold theory, Tensors, Semi-Riemannian Manifolds; Isometries,Levi-Civita connection,paralel translation, geodesics, the exponential mapping, curvature, sectional curvature, Semi-Riemann surfaces, Semi-Riemannian Submanifolds; Ricci and scalar curvature, Semi-Riemann product manifolds, local isometries, Riemannian and Lorentz Geometry; Gauss lemma, convex open sets, arclength, Riemaniann distance, Lorentz causal character, time cone, Local Lorentz geometry, geodesics,completeness and extendibility, Constructions; Deck transformations, volume elements, vector bundles, local isometries, Warped products, Isometries; isometry groups, space forms, homogeneous spaces |
Weekly Detailed Course Contents
| Week | Subject | Related Preparation |
| 1) | Preliminiars and Manifold theory | |
| 2) | Manifold theory | |
| 3) | Tensors | |
| 4) | Tensors | |
| 5) | Semi-Riemannian Manifolds; Isometries,Levi-Civita connection,paralel translation, geodesics, the exponential mapping, curvature, sectional curvature, Semi-Riemann surfaces | |
| 6) | Semi-Riemannian Submanifolds; Ricci and scalar curvature | |
| 7) | Semi-Riemann product manifolds, local isometries | |
| 8) | Riemannian and Lorentz Geometry; Gauss lemma, convex open sets, arclength, Riemaniann distance | |
| 9) | Lorentz causal character, time cone | |
| 10) | Local Lorentz geometry, geodesics,completeness and extendibility | |
| 11) | Constructions; Deck transformations, volume elements, vector bundles, local isometries | |
| 12) | Warped products | |
| 13) | Isometries; isometry groups, space forms | |
| 14) | homogeneous spaces |
Sources
| Course Notes / Textbooks: | Semi-Riemannian Geometry With Applications to Relativity,Barrett O'Neill, 103 Academic Press, ISBN: 0125267401 |
| References: | . |
Evaluation System
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | 14 | % 5 |
| Homework Assignments | 3 | % 15 |
| Midterms | 2 | % 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 |
| Homework Assignments | 3 | 25 | 75 |
| Midterms | 2 | 30 | 60 |
| Final | 1 | 25 | 25 |
| Total Workload | 202 | ||
Contribution of Learning Outcomes to Programme Outcomes
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |