Differential Geometry (MATH7435)
Course level
Postgraduate Coursework
Faculty
School
Mathematics & Physics School
Units
2
Duration
One Semester
Class hours
Lecture 3 Hours/ Week
Tutorial 1 Hour/ Week
3L:1T
Incompatible
MATH3405 (co-taught).
Prerequisite
Knowledge equivalent to MATH7000
Recommended prerequisite
Knowledge equivalent to MATH7400 or MATH7407, MATH7307
Assessment methods
Examination
Assignments
Course enquiries
Dr Ramiro Lafuente
Current course offerings
Course offerings | Location | Mode | Course Profile |
Semester 2, 2024 (22/07/2024 - 18/11/2024) | St Lucia | In Person | Profile unavailable |
Please Note: Course profiles marked as not available may still be in development.
Course description
Curves: Parameterised curves, regular curves, arc length. Local theory, Frenet frame. Global properties of plane curves. Regular surfaces: Change of parameterisation, differential functions on surfaces. The tangent plane, the differential of a map. First fundamental form, area functional. Geometry of the Gauss map: fundamental properties, local coordinates. Vector fields. Minimal surfaces and other applications. Intrinsic and extrinsic geometry of surfaces: isometries, conformal maps. Selected topics from: Theorema egregium. Parallel transport, geodesics. Gauss-Bonnet Theorem and applications. Exponential map. Geodesic polar coordinates. Introduction to smooth manifolds.
Archived offerings
Course offerings | Location | Mode | Course Profile |
Semester 2, 2023 (24/07/2023 - 18/11/2023) | External | External | Profile unavailable |
Semester 2, 2023 (24/07/2023 - 18/11/2023) | St Lucia | In Person | Course Profile |
Semester 2, 2022 (25/07/2022 - 19/11/2022) | External | External | Course Profile |
Semester 2, 2022 (25/07/2022 - 19/11/2022) | St Lucia | Internal | Course Profile |