Specialized Topics in Geometry (ΓΕ8)
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General
| School | School of Science |
|---|---|
| Academic Unit | Department of Mathematics |
| Level of Studies | Graduate |
| Course Code | ΓΕ8 |
| Semester | 2 |
| Course Title | Special Topics in Geometry |
| Independent Teaching Activities | Lectures (Weekly Teaching Hours: 3, Credits: 7.5) |
| Course Type | Special Background |
| Prerequisite Courses | - |
| Language of Instruction and Examinations |
Greek |
| Is the Course Offered to Erasmus Students | Yes (in English) |
| Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
| Learning outcomes |
In this lecture we discuss several topics concerning contemporary topics in Differential Geometry, e.g. symplectic and Kähler manifolds, theory of isometric immersions, minimal surfaces and geometric evolution equations. |
|---|---|
| General Competences |
|
Syllabus
- Complex manifolds.
- Kählerian manifolds.
- Riemannian submersions and projective spaces.
- Homogeneous and symmetric spaces.
- Holonomy groups.
- The Bochner technique.
- Harmonic maps and harmonic forms.
- Minimal submanifolds.
- Convergence of Riemannian manifolds.
- Comparison theorems.
- Geometric flows.
Teaching and Learning Methods - Evaluation
| Delivery |
Face-to-face | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Use of Information and Communications Technology | - | ||||||||||
| Teaching Methods |
| ||||||||||
| Student Performance Evaluation |
Weakly homeworks, presentations. |
Attached Bibliography
- B. Andrews and C. Hopper, The Ricci flow in Riemannian Geometry, Springer, 2011.
- T. Colding and W. Minicozzi, A course in minimal surfaces, Graduate Studies in Mathematics, Volume 121, 2011.
- M. Dajczer and R. Tojeiro, Submanifolds theory beyond an introduction, Springer, 2019.
- J. Jost, Riemannian Geometry and Geometric Analysis, 7th edition, Springer, 2017.
- P. Petersen, Riemannian Geometry, 3rd edition, Graduate Texts in Mathematics, 171, Springer, 2016.