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School of Science
Department of Mathematics
|Level of Studies||
|Independent Teaching Activities||
Lectures, laboratory exercises (Weekly Teaching Hours: 3, Credits: 6)
|Language of Instruction and Examinations||
|Is the Course Offered to Erasmus Students||
|Course Website (URL)||See eCourse, the Learning Management System maintained by the University of Ioannina.|
In this lecture we introduce basic notions of modern Differential Geometry. More precisely, we introduce among others the notions of manifold, tangent bundle, connection, parallel transport and Riemannian metric.
- Smooth manifolds.
- Smooth maps.
- Tangent vectors.
- Vector fields.
- Regular values and Sard's Theorem.
- Homotopy and Isotopy.
- Lie bracket.
- Frobenius' Theorem.
- Connections and parallel transport.
- Riemannian metrics.
Teaching and Learning Methods - Evaluation
|Use of Information and Communications Technology||-|
|Student Performance Evaluation||
Weakly homeworks and written final examination.
- M. do Carmo, Riemannian Geometry, Birkhaüser Boston, Inc., Boston, MA, 1992.
- V. Guillemin & A. Pollack, Differentiable Topology, Prentice-Hall, Inc, Englewood Cliffs, 1974.
- J. Lee, Introduction to Smooth Manifolds, Graduate Texts in Mathematics, 218, 2013.
- J. Milnor, Topology From the Differentiable Viewpoint, Princeton University Press, NJ, 1997.
- L. Tu, An Introduction to Manifolds, Universitext. Springer, New York, 2011.
- Δ. Κουτρουφιώτης, Διαφορική Γεωμετρία, Πανεπιστήμιο Ιωαννίνων, 1994.