Elementary Differential Geometry (MAY522)

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School of Science

Academic Unit

Department of Mathematics

Level of Studies


Course Code


Semester 5
Course Title

Elementary differential geometry

Independent Teaching Activities

Lectures (Weekly Teaching Hours: 5, Credits: 7.5)

Course Type

General 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 differential geometry. The aim is to introduce and study geometric properties of regular curves (both plane and space) and regular surfaces. Fundamental notions of differential geometry of curves and surfaces are introduced and studied. Among them is the notion of curvature. The study requires tools from Linear Algebra and Calculus of several variables.
Upon completion of the course, the student should be familiar with basic notions of differential geometry like the one of curvature, first and second fundamental form, isometries between surfaces and their geometric meaning.

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


  • Plane curves, arclength, curvature, Frenet frame.
  • Space curves, curvature and torsion, Frenet frame, fundamental theorem of curves.
  • Surfaces, parametrization, Gauss map, Weingarten map, first and second fundamental form, normal curvature, principal and asymptotic directions, Gaussian and mean curvature, minimal surfaces, Theorema Egregium, Gauss and Weingarten formulas, fundamental theorem of surfaces, developable surfaces.

Teaching and Learning Methods - Evaluation



Use of Information and Communications Technology -
Teaching Methods
Activity Semester Workload
Lectures 65
Autonomous study 127.5
Course total 187.5
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