MAT 645 
Topics in Differential Geometry 
Spring 2023 

TΘ 1:15-2:35
Physics P-127

Prof. Claude LeBrun.
Office: Math Tower 3-108.
Office hours: TΘ 2:45-4:15 pm,
or by appointment.

Twistor Methods in Differential Geometry

This course will offer a self-contained introduction to twistor correspondences in Riemannian and pseudo-Riemannian geometry. Topics will include: self-dual 4-manifolds, self-dual Einstein metrics, hyper-Kähler manifolds, manifolds whose geodesics are all closed, and Einstein-Weyl geometry in dimension 3.

The course will presuppose a basic knowledge of Riemannian geometry, say on the level of MAT 568, Differential Geometry I. Some basic knowledge of complex manifolds, for example on the level of MAT 645, Complex Geometry, would also be extremely helpful.

Grades will be based upon attendance and class participation.

The Professor may be reach by e-mail by .
This is the best method for making appointments outside normal office hours.

Illustration: Ruling lines on a quadric surface.

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