Differential Geometry (ΓΕ2)

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Graduate Courses Outlines - Department of Mathematics

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
  1. Work autonomously
  2. Work in teams
  3. 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

  1. Manfredo do Carmo, Riemannian geometry, Birkauser, 1992.
  2. John M. Lee, Introduction to smooth manifolds, Springer, 2013.
  3. M. Spivak, A comprehensive introduction to differential geometry, Publish or Perish, 1979.