Differential Geometry (ΓΕ2)
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Graduate Courses Outlines - Department of Mathematics
General
| School | School of Science |
|---|---|
| Academic Unit | Department of Mathematics |
| Level of Studies | Graduate |
| Course Code | ΓΕ2 |
| Semester | 1 |
| Course Title | Differential Geometry |
| Independent Teaching Activities | Lectures (Weekly Teaching Hours: 3, Credits: 7.5) |
| Course Type | Special Background |
| Prerequisite Courses |
Linear Algebra, Topology, Calculus of Several Variables. |
| 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 Differential Geometry. More precisely, we introduce among others the notions of manifold, manifold with boundary, vector bundle, connection, parallel transport, submanifold, differential form and de Rham cohomology. |
|---|---|
| General Competences |
|
Syllabus
- Topological and smooth manifolds.
- Tangent and cotangent bundles.
- Vector fields and their flows.
- Submanifolds and Frobenius’ Theorem.
- Vector bundles.
- Connection and parallel transport.
- Differential forms.
- De Rham cohomology.
- Integration.
- Stokes’ Theorem.
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, presentation in the blackboard of the HomeWorks, 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.