Global Differential Geometry
| Title | ΟΛΙΚΗ ΔΙΑΦΟΡΙΚΗ ΓΕΩΜΕΤΡΙΑ / Global Differential Geometry |
| Code | 0655 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Spring |
| Coordinator | Manousos Maridakis |
| Common | Yes |
| Status | Active |
| Course ID | 40000043 |
Programme of Study: PMS Tmīmatos Mathīmatikṓn (2018-sīmera)
Registered students: 0
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| THEŌRĪTIKA MATHĪMATIKA | Core Courses A3 | 2 | 1 | 10 |
| Academic Year | 2017 – 2018 |
| Class Period | Winter |
| Faculty Instructors | |
| Weekly Hours | 3 |
| Class ID | 600112021
|
Course Type 2016-2020
- Scientific Area
Course Type 2011-2015
Specific Foundation / Core
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600112021
- At the Website of the School: users.auth.gr/stamata
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
- English (Examination)
- French (Examination)
- German (Examination)
General Competences
- Work autonomously
- Work in teams
- Work in an international context
- Work in an interdisciplinary team
- Generate new research ideas
Course Content (Syllabus)
Elements of the theory of differentiable manifolds. Triangulation of manifolds. Closed surfaces. Chatacterizations of the sphere (Theorems of Liebmann e.tc.). The Gauss-Bonnet theorem and its applications. Integral formulae of Μinkowski. The index method (Poincaré). Congruence theorems for ovaloids. Rigitidy of ovaloids. Uniqueness theorems for the problems of Christoffel and Minkowski. The maximum-principle method. Complete surfaces. Theorem of Hopf-Rinow. Inequality of Cohn-Vossen.
Keywords
Global differential geometry
Educational Material Types
- Notes
- Slide presentations
- Book
Use of Information and Communication Technologies
Use of ICT
- Use of ICT in Communication with Students
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 30 | 1 | ✓ | ||
| Seminars | ✓ | ||||
| Reading Assigment | ✓ | ||||
| Tutorial | 9 | 0.3 | ✓ | ✓ | |
| Project | ✓ | ||||
| Total | 39 | 1.3 |
Student Assessment
Description
Written examination
Student Assessment methods
- Written Exam with Short Answer Questions (Formative, Summative)
- Written Assignment (Formative, Summative)
- Written Exam with Problem Solving (Formative, Summative)
Bibliography
Additional bibliography for study
- Blaschke W., Leichtweiss K.: Elementare Differentialgeometrie. Springer, 1970
- Hopf, H.: Differential Geometry in the Large. LNM, Band 1000. Springer, 1983
- Hsiung C.C.: A first Course in Differential Geometry. Wiley, 1981
- Huck H., Roitzsch R., Simon U., Vortisch W., Walden R., Wegner B., Wendland W.: Beweismethoden der Differentialgeometrie im Grossen. LNM, Band 335. Springer, 1973
- Klingenberg W.: Klassische Differentialgeometrie. EAG, 2004
- Kühnel W.: Differential Geometry. Curves – Surfaces – Manifolds. AMS 2002
- O’ Neill B.: Elementary Differential Geometry. Academic Press , 1966
- O’ Neill B.: Στοιχειώδης Διαφορική Γεωμετρία. Π.Ε.Κ. 2002
- Στεφανίδη Ν.: Διαφορική Γεωμετρία, τ. 2, 1995
- Stoker J.J.: Differential Geometry. Wiley-Interscience, 1969
- Švec A.: Global Differential Geometry of Surfaces. VEB 1981
- Voss K.: Differentialgeometrie geschlossener Flächen im Euklidischen Raum, Jahresbericht der DMV 63, 117-135 (1960)
- Willmore T. J.: An introduction to differential geometry. Oxford, 1959
Last Update
20-09-2013
