Differential Geometry (MATH3405)
Information valid for Semester 2, 2024
Course level
Undergraduate
Faculty
School
Mathematics & Physics School
Units
2
Duration
One Semester
Attendance mode
In Person
Class hours
Lecture 3 Hours/ Week
Tutorial 1 Hour/ Week
3L1T
Incompatible
MATH7435 (co-taught).
Prerequisite
MATH2000 or MATH2001
Recommended prerequisite
(MATH2400 or MATH2401), MATH2301
Assessment methods
Assignments and examination
Course enquiries
Dr Ramiro Lafuente
Study Abroad
This course is pre-approved for Study Abroad and Exchange students.
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.