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, Elementary differential geometry, Calculus, Analysis of several variables.
|
| Language of Instruction and Examinations
|
Greek
|
| Is the Course Offered to Erasmus Students
|
Yes (in English)
|
| Course Website (URL)
|
-
|
Learning Outcomes
| Learning outcomes
|
This course introduces the basic notions of differential and Riemannian geometry.
|
| General Competences
|
- Work autonomously
- Work in teams
- Develop critical thinking skills.
|
Syllabus
Differentiable manifolds, immersions, embeddings, submanifolds, vector fields, orientation covering spaces, partition of unity, Riemannian manifolds, Levi-Civita connection, curvature tensor, geodesics, exponential map, Isometric immersions, second fundamental form, hypersurfaces, Gauss, Codazzi and Ricci equations, applications.
Teaching and Learning Methods - Evaluation
| Delivery
|
Direct
|
| Use of Information and Communications Technology
|
-
|
| Teaching Methods
|
| Activity
|
Semester Workload
|
| Lectures
|
39
|
| Study and analysis of bibliography
|
78
|
| Preparation of assignments and interactive teaching
|
70.5
|
| Course total
|
187.5
|
|
| Student Performance Evaluation
|
Written final examination.
|
Attached Bibliography
- Manfredo do Carmo, Riemannian geometry, Birkauser, 1992.
- John M. Lee, Introduction to smooth manifolds, Springer, 2013.
- M. Spivak, A comprehensive introduction to differential geometry, Publish or Perish, 1979.