Classical Differential Geometry (ΓΕ1)
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General
| School | School of Science |
|---|---|
| Academic Unit | Department of Mathematics |
| Level of Studies | Graduate |
| Course Code | ΓΕ1 |
| Semester | 1 |
| Course Title | Classical Differential Geometry |
| Independent Teaching Activities | Lectures (Weekly Teaching Hours: 3, Credits: 7.5) |
| Course Type | Special Background |
| Prerequisite Courses |
Topology, Calculus of Several Variables, Complex Analysis. |
| 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 introduce basic notions of Classical Differential Geometry. More precisely, we introduce among others the notions of a manifold as a subset of the Euclidean space. Then, we present various local and global theorems concerning minimal submanifolds. |
|---|---|
| General Competences |
|
Syllabus
- Manifolds of the Euclidean space.
- Tangent and normal bundles.
- 1st and 2nd fundamental forms.
- Weingarten operator and Gauss map.
- Convex hypersurfaces.
- Hadamard’s Theorem.
- 1st and 2nd variation of area.
- Minimal submanifolds.
- Weierstrass representation.
- Bernstein’s Τheorem.
Teaching and Learning Methods - Evaluation
| Delivery |
Face-to-face. | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Use of Information and Communications Technology | - | ||||||||||
| Teaching Methods |
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| Student Performance Evaluation |
Weakly HomeWorks, presentations of the HomeWorks in the blackboard, written final examination. |
Attached Bibliography
- M. do Carmo, Riemannian Geometry, Birkhaüser Boston, Inc., Boston, MA, 1992.
- J. Jost, Riemannian Geometry and Geometric Analysis, Universitext, Springer, 2017.
- J. Lee, Introduction to smooth manifolds, Second edition, Graduate Texts in Mathematics, 218, Springer, 2013.
- Δ. Κουτρουφιώτης, Διαφορική Γεωμετρία, Πανεπιστήμιο Ιωαννίνων, 1994.