Lecture Notes in Mathematics

3 primary works

Geometry Seminar "Luigi Bianchi" II - 1984

by Mauro Meschiari, John H. Rawnsley, and Simon Salamon

Published 1 December 1985

Twistor Theory for Riemannian Symmetric Spaces

by Francis E. Burstall and John H. Rawnsley

Published 22 May 1990

In this monograph on twistor theory and its applications to harmonic map theory, a central theme is the interplay between the complex homogeneous geometry of flag manifolds and the real homogeneous geometry of symmetric spaces. In particular, flag manifolds are shown to arise as twistor spaces of Riemannian symmetric spaces. Applications of this theory include a complete classification of stable harmonic 2-spheres in Riemannian symmetric spaces and a Backlund transform for harmonic 2-spheres in Lie groups which, in many cases, provides a factorisation theorem for such spheres as well as gap phenomena. The main methods used are those of homogeneous geometry and Lie theory together with some algebraic geometry of Riemann surfaces. The work addresses differential geometers, especially those with interests in minimal surfaces and homogeneous manifolds.

Conformal Geometry of Surfaces in S4 and Quaternions

by Francis E. Burstall, Dirk Ferus, Katrin Leschke, Franz Pedit, and Ulrich Pinkall

Published 1 January 2002

The conformal geometry of surfaces recently developed by the authors leads to a unified understanding of algebraic curve theory and the geometry of surfaces on the basis of a quaternionic-valued function theory. The book offers an elementary introduction to the subject but takes the reader to rather advanced topics. Willmore surfaces in the foursphere, their Backlund and Darboux transforms are covered, and a new proof of the classification of Willmore spheres is given.