Francis E. Burstall - Böcker
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2 produkter
2 produkter
Del 1772 - Lecture Notes in Mathematics
Conformal Geometry of Surfaces in S4 and Quaternions
Häftad, Engelska, 2002
378 kr
Skickas inom 10-15 vardagar
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 Bäcklund and Darboux transforms are covered, and a new proof of the classification of Willmore spheres is given.
Del 1424 - Lecture Notes in Mathematics
Twistor Theory for Riemannian Symmetric Spaces
With Applications to Harmonic Maps of Riemann Surfaces
Häftad, Engelska, 1990
272 kr
Skickas inom 10-15 vardagar
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 factorization 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.