Elementary Global Differential Geometry (MAE624)

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School of Science

Academic Unit

Department of Mathematics

Level of Studies


Course Code




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


Is the Course Offered to Erasmus Students

Yes (in English)

Course Website (URL) See eCourse, the Learning Management System maintained by the University of Ioannina.

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
  • Work autonomously
  • Work in teams
  • Develop critical thinking skills


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



Use of Information and Communications Technology -
Teaching Methods
Activity Semester Workload
Lectures 39
Autonomous study 111
Course total 150
Student Performance Evaluation

Written final examination

Attached Bibliography

See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:

  • Barrett O' Neil, Στοιχειώδης Διαφορική Γεωμετρία, Πανεπιστημιακές Εκδόσεις Κρήτης, 2002
  • Manfredo do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, 1976