Elementary Global Differential Geometry (MAE624)
General
| School |
School of Science |
|---|---|
| Academic Unit |
Department of Mathematics |
| Level of Studies |
Undergraduate |
| Course Code |
MAE624 |
| Semester |
6 |
| Course Title |
Elementary Global Differential Geometry |
| Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
| 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) | - |
Learning Outcomes
| Learning outcomes |
It is an introductory course on global differential geometry. The aim is to study global geometric properties of regular plane curves and regular surfaces. The study requires tools from Linear Algebra, Calculus of several variables, Topology and elementary differential geometry. On completion of the course the student should be familiar with the interplay between local and global properties of curves and surfaces. |
|---|---|
| General Competences |
|
Syllabus
Convex curves, Hopf's Umlaufsatz, Four vertex theorem, isoperimetric inequality. Surfaces, vector fields, covariant derivative, parallel transport, geodesic curvature, geodesics, exponential map, surfaces of constant Gaussian curvature, Gauss Bonnet Theorem, Liebmann Theorem.
Teaching and Learning Methods - Evaluation
| Delivery |
Direct | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Use of Information and Communications Technology | - | ||||||||
| Teaching Methods |
| ||||||||
| Student Performance Evaluation |
Written final examination |
Attached Bibliography
- Δ. Κουτρουφιώτης, Στοιχειώδης Διαφορική Γεωμετρία, Εκδόσεις Leader Books, 2006
- Barrett O' Neil, Στοιχειώδης Διαφορική Γεωμετρία, Πανεπιστημιακές Εκδόσεις Κρήτης, 2002
- Andrew Pressley, Στοιχειώδης Διαφορική Γεωμετρία, Πανεπιστημιακές Εκδόσεις Κρήτης, 2011
- Manfredo do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, 1976