2017/18 Taught Postgraduate Module Catalogue

MATH5113M Advanced Differential Geometry

20 creditsClass Size: 30

Module manager: Dr Gerasim Kokarev
Email: G.Kokarev@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2017/18

Pre-requisites

MATH2051

Geometry of Curves and Surfaces

This module is mutually exclusive with

MATH3113

Differential Geometry

This module is approved as an Elective

Module summary

*

Objectives

To further the study of curves and surfaces, in particular, to understand what properties of curves and surfaces are intrinsic, extrinsic, local, or global, and to give some applications.

Several topics will be taken further than Differential Geometry, and an understanding of basic ideas of abstract Riemannian Geometry will be gained.

Syllabus

- Plane curves: rotation index, isoperimetric inequality, Fenchel's theorem.
- Space curves: congruence, total curvature of a knot.
- Submanifolds of Euclidean spaces as level sets, Gauss map.
- Curves on a surface, geodesics.
- Gauss Lemma and a proof that geodesics minimise distance locally.
- Isometries and conformal maps.
- Theorema Egregrium. Gauss-Bonnet theorem. Abstract Riemannian metrics.

Teaching methods

Delivery type	Number	Length hours	Student hours
Lecture	44	1.00	44.00
Private study hours			156.00
Total Contact hours			44.00
Total hours (100hr per 10 credits)			200.00

Private study

Studying and revising of course material.
Completing of assignments and assessments.

Opportunities for Formative Feedback

Regular problem sheets

Methods of assessment

Exams

Exam type	Exam duration	% of formal assessment
Standard exam (closed essays, MCQs etc)	3 hr 00 mins	100.00
Total percentage (Assessment Exams)		100.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Reading list

The reading list is available from the Library website

Last updated: 26/04/2017

Disclaimer

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