# Elementary Differential Geometry (MAY522)

### General

School School of Science Department of Mathematics Undergraduate MAY522 5 Elementary differential geometry Lectures (Weekly Teaching Hours: 5, Credits: 7.5) General Background - Greek Yes (in English) 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. Work autonomously Work in teams Develop critical thinking skills

### Syllabus

• 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

Delivery

Direct

Use of Information and Communications Technology -
Teaching Methods