MATH426-18S1 (C) Semester One 2018

Differential Geometry

15 points

Details:
Start Date: Monday, 19 February 2018
End Date: Sunday, 24 June 2018
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Friday, 2 March 2018
  • Without academic penalty (including no fee refund): Friday, 18 May 2018

Description

Differential Geometry

Have you ever wondered why you can roll a piece of paper into a tube but cannot bend the paper tube to form a torus without wrinkling or breaking the paper or how a Ôflat beingÕ can decide whether it lives on a 2-sphere or a torus? There are physical reasons to the first question but differential geometry also provides a mathematical answer to both.

The principal objects of interest in differential geometry are differentiable manifolds, like a sphere or a torus, that may be equipped with additional structures, like a metric or a group structure, which leads to Riemannian geometry or Lie groups, respectively. One then investigates intrinsic properties of differentiable manifolds and their invariants. In so doing one encounters many ideas which are not only beautiful in themselves but are basic for both advanced mathematics and theoretical physics.

The course gives an introduction to classical differential geometry including the basic theory of manifolds, vector fields, geodesics and intrinsic invariants like curvature, and how Lie groups feature in this context.

Prerequisites

Subject to approval of the Head of School.

Course Coordinator

Gunter Steinke

Indicative Fees

Domestic fee $950.00

* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.

For further information see Mathematics and Statistics .

All MATH426 Occurrences

  • MATH426-18S1 (C) Semester One 2018