Elementary Global Differential Geometry (MAE624)

Undergraduate Courses Outlines - Department of Mathematics

General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Undergraduate
Course Code	MAE624
Semester	6
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	Greek
Is the Course Offered to Erasmus Students	Yes (in English)
Course Website (URL)	-

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

Syllabus

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

Delivery	Direct
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 Eudoxus. Additionally:

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