Classical Differential Geometry II
| Title | ΚΛΑΣΙΚΗ ΔΙΑΦΟΡΙΚΗ ΓΕΩΜΕΤΡΙΑ ΙΙ / Classical Differential Geometry II |
| Code | 0332 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Spring |
| Common | Yes |
| Status | Active |
| Course ID | 40000470 |
Programme of Study: UPS of School of Mathematics (2014-today)
Registered students: 15
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| Core | Elective Courses belonging to the selected specialization | Spring | - | 5.5 |
| Academic Year | 2020 – 2021 |
| Class Period | Spring |
| Faculty Instructors |
|
| Weekly Hours | 3 |
| Class ID | 600166745
|
Course Type 2016-2020
- Scientific Area
Course Type 2011-2015
Specific Foundation / Core
Mode of Delivery
- Face to face
- Distance learning
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600166745
- eLearning (Moodle): https://elearning.auth.gr/course/view.php?id=15094
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
- English (Instruction, Examination)
- French (Instruction, Examination)
- German (Instruction, Examination)
Prerequisites
Required Courses
- 0108 Linear Algebra
- 0303Α Classical Differential Geometry I
Learning Outcomes
Upon successful completion of the course, students will be able to:
1) Use the notion of covariant derivative between vector fields and understand its functionality on a surface.
2) Compute and identify geodesic curves of a surface. They will also be able to ompute the geodesic curvature.
3) Apply the Gauss - Bonnet Theorem.
4) Distinguish between the spaces of constant curvature and their individual features.
5) Demonstrate these features on the basic models of such spaces.
General Competences
- Apply knowledge in practice
- Make decisions
- Work autonomously
- Work in teams
- Work in an international context
- Work in an interdisciplinary team
- Generate new research ideas
- Advance free, creative and causative thinking
Course Content (Syllabus)
Reminder of basic constructions of Differential Geometry (principal and mean curvature, Gauss curvature, normal and geodesic curvature), covariant derivative and geodesic curves, length functional, Clairaut's Theorem, local and global Gauss-Bonnet Theorem, surfaces of constant curvature, topological structure of surfaces, Euler characteristic.
Keywords
Curvature, Gauss-Bonnet Theorem, Euler characteristic.
Educational Material Types
- Notes
- 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 | 130 | 4.3 | ✓ | ✓ | |
| Reading Assigment | 15 | 0.5 | ✓ | ✓ | ✓ |
| Tutorial | 18 | 0.6 | ✓ | ✓ | ✓ |
| Exams | 3 | 0.1 | ✓ | ✓ | ✓ |
| Total | 166 | 5.5 |
Student Assessment
Description
Written examination
Student Assessment methods
- Written Assignment (Summative)
- Written Exam with Problem Solving (Summative)
Bibliography
Course Bibliography (Eudoxus)
- A. Pressley: Στοιχειώδης Διαφορική Γεωμετρία.Ηράκλειο : Πανεπιστημιακές Εκδόσεις Κρήτης, 2011
- B. O'Neill: Στοιχειώδης Διαφορική Γεωμετρία, Ηράκλειο : Πανεπιστημιακές Εκδόσεις Κρήτης, 2002
- Α. Αρβανιτογεώργος: Στοιχειώδης Διαφορική Γεωμετρία, Σύνδεσμος Ελληνικών Ακαδημαϊκών Βιβλιοθηκών, 2015
- Σ. Σταματάκης: Εισαγωγή στην Κλασική Διαφορική Γεωμετρία, Θεσσαλονίκη, Εκδόσεις Αϊβάζη, 2008
- Δ. Κουτρουφιώτης: Στοιχειώδης διαφορική γεωμετρία, Αθήνα : Leader Books, 2006
Additional bibliography for study
- M. Abate, F. Tovena: Curves and Surfaces. Springer, 2012
- M. P. do Carmo: Differential Geometry of Curves and Surfaces. Prentice – Hall, 1976
- J. Oprea: Differential Geometry and its Applications. Prentice Hall, 1997
Last Update
06-02-2021
