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Information
| Code | MT0028 |
| Name | Structures on Manifolds |
| Term | 2024-2025 Academic Year |
| Semester | . Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Yüksek Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. NERGİZ POYRAZ |
Course Goal / Objective
The aim of this course is to provide basic knowledge about the geometry of manifolds.
Course Content
Differentiable manifolds, Vector Bundles, Distributions, Riemannian Manifolds, Riemannian Submanifolds, Almost Complex Structures, Contact Structures
Course Precondition
None
Resources
1. Aurel Bejancu, Geometry of CR-Submanifolds, D. Reidel Pu. Comp., 1986. 2.David E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Birkhauser, Boston, Basel, Berlin, 2001. 3. Kentaro Yano, Masahiro Kon, Structures on Manifolds, Series in Pure Math.-Vol.3, World Sci. Pub. 1984.
Notes
1. Aurel Bejancu, Geometry of CR-Submanifolds, D. Reidel Pu. Comp., 1986.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Comprehends the concept of Differentiable Manifolds. |
| LO02 | Understands Vector Bundles and Distribution Concepts. |
| LO03 | Knows Riemann Manifolds and Riemann Connections. |
| LO04 | Comprehends the Concepts of Complex Structures and Complex Manifolds. |
| LO05 | Almost Understands the Concepts of Complex Manifolds. |
| LO06 | Kaehler Knows the Concept of Manifolds. |
| LO07 | Knows Sasakian Manifolds Concept. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in her area of expertise and other areas of mathematics. | 3 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in his area of expertise and other areas of mathematics. | 4 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Establishes new mathematical models with the help of the knowledge gained in the field of specialization. | 2 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Has basic knowledge in all areas of mathematics. | |
| PLO05 | Bilgi - Kuramsal, Olgusal | It presents the knowledge gained in different fields of mathematics and their relations with each other in the simplest and most understandable way. | 3 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Effectively uses the technical equipment needed to express mathematics. | |
| PLO07 | Bilgi - Kuramsal, Olgusal | poses original problems related to field and presents different solution techniques. | 2 |
| PLO08 | Bilgi - Kuramsal, Olgusal | carries out original and qualified scientific studies on the subject related to its field. | 3 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Analyzes existing mathematical theories and develops new theories. | |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | Knows the teaching-learning techniques in areas of mathematics that require expertise and uses these techniques effectively at every stage of education. | |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | To have knowledge of a foreign language at a level to be able to follow foreign sources related to the field and to communicate verbally and in writing with foreign stakeholders. | 4 |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | presents and publishes its original works within the framework of scientific ethical rules for the benefit of its stakeholders. | 2 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Adheres to the ethical rules required by its scientific title | 5 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Some Reminders About Differentiable Manifolds | Pages related to the subject in the source books | Öğretim Yöntemleri: Anlatım, Tartışma |
| 2 | Vector Bundles | Pages related to the subject in the source books | Öğretim Yöntemleri: Anlatım, Tartışma |
| 3 | Distributions | Pages related to the subject in the source books | Öğretim Yöntemleri: Anlatım, Tartışma |
| 4 | Affine Connections | Pages related to the subject in the source books | Öğretim Yöntemleri: Anlatım, Tartışma |
| 5 | Riemann Manifolds and Riemann Connections | Pages related to the subject in the source books | Öğretim Yöntemleri: Anlatım, Tartışma |
| 6 | Riemann Submanifolds and Curvatures | Pages related to the subject in the source books | Öğretim Yöntemleri: Anlatım, Tartışma |
| 7 | Complex Structures and Complex Manifolds | Pages related to the subject in the source books | Öğretim Yöntemleri: Anlatım, Tartışma |
| 8 | Mid-Term Exam | All topics covered up to week 7 in recommended resources | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Almost Complex Manifolds | Pages related to the subject in the source books | Öğretim Yöntemleri: Anlatım, Tartışma |
| 10 | Hermitian Manifolds | Pages related to the subject in the source books | Öğretim Yöntemleri: Anlatım, Tartışma |
| 11 | Kaehler Manifolds | Pages related to the subject in the source books | Öğretim Yöntemleri: Anlatım, Tartışma |
| 12 | Contact Manifolds | Pages related to the subject in the source books | Öğretim Yöntemleri: Anlatım, Tartışma |
| 13 | Almost Contact Manifolds | Pages related to the subject in the source books | Öğretim Yöntemleri: Anlatım, Tartışma |
| 14 | Sasakian Manifolds | Pages related to the subject in the source books | Öğretim Yöntemleri: Anlatım, Tartışma |
| 15 | an overwiev | an overwiev | Öğretim Yöntemleri: Anlatım |
| 16 | Term Exams | All topics in Source Books | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | All topics in Source Books | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 13 | 3 | 39 |
| Out of Class Study (Preliminary Work, Practice) | 13 | 5 | 65 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 3 | 5 | 15 |
| Mid-term Exams (Written, Oral, etc.) | 0 | 0 | 0 |
| Final Exam | 1 | 25 | 25 |
| Total Workload (Hour) | 144 | ||
| Total Workload / 25 (h) | 5,76 | ||
| ECTS | 6 ECTS | ||