Geometry (2010/2011)

Course code
4S00247
Name of lecturer
Mauro Spera
Coordinator
Mauro Spera
Number of ECTS credits allocated
6
Academic sector
MAT/03 - GEOMETRY
Language of instruction
Italian
Location
VERONA
Period
II semestre dal Mar 1, 2011 al Jun 15, 2011.

Lesson timetable

Learning outcomes

Learning objectives

The course introduces and elaborates the fundamental ideas of general topology and of the differential geometry of curve and surfaces, in a rigorous yet concrete and
example-based manner, so as to further develop the students' geometric intuition,
abstraction and analytical computing ability, also in view of applications to parallel and successive courses.

Syllabus

*Programme
Topological spaces, continuous functions, omeomorphisms.
Compactness. Connectedness.
Plane and spatial curves: curvature, torsion, Fre'net's formulae. Fundamental theorem.
Regular parametric surfaces. First and second fundamental form.
Gaussian and mean curvature.
Gauss' Theorema Egregium. Covariant derivative, parallel transport.
Geodesics. The Gauss-Bonnet theorem.
Examples: quadrics, surfaces of revolution, ruled and minimal surfaces.
Projective, affine and metric classification of quadrics.

Assessment methods and criteria

Assessment

Written test, followed by an oral exam.