✦ LIBER ✦

Conformal Geometry of Surfaces in Quaternions

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

Book ID: 127447215
Publisher: Springer
Year: 2002
Tongue: English
Weight: 4 MB
Edition: 1
Category: Library
ISBN-13: 9783540430087

No coin nor oath required. For personal study only.

✦ Synopsis

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.

📜 SIMILAR VOLUMES

Surfaces in Conformal Geometry

✍ T. J. Willmore 📂 Article 📅 2000 🏛 Springer 🌐 English ⚖ 81 KB

Generalised quaternion methods in confor

Generalised quaternion methods in conformal geometry

✍ Eric A. Lord 📂 Article 📅 1975 🏛 Springer 🌐 English ⚖ 794 KB

Conformal geometry of surfaces in Lorent

Conformal geometry of surfaces in Lorentzian space forms

✍ L. J. Alĺas; B. Palmer 📂 Article 📅 1996 🏛 Springer 🌐 English ⚖ 579 KB

We study the conformal geometry of an oriented space-like surface in three-dimensional Lorentzian space forms. After introducing the conformal compactification of the Lorentzian space forms, we define the conformal Gauss map which is a conformally invariant two parameter family of oriented spheres.

Quaternionic geometry of matroids

✍ Tamás Hausel 📂 Article 📅 2005 🏛 SP Versita 🌐 English ⚖ 280 KB

The Geometry of Polygons in ℝ5and Quater

The Geometry of Polygons in ℝ5and Quaternions

✍ Philip Foth; Guadalupe Lozano 📂 Article 📅 2004 🏛 Springer 🌐 English ⚖ 218 KB

A Conformal Field Theory of Extrinsic Ge

A Conformal Field Theory of Extrinsic Geometry of 2-d Surfaces

✍ K.S. Viswanathan; R. Parthasarathy 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 665 KB

In the description of the extrinsic geometry of the string world sheet regarded as a conformal immersion of a \(2-\mathrm{d}\) surface in \(R^{3}\), it was previously shown that restricting ourselves to surfaces with \(h \sqrt{g}=1\), where \(h\) is the mean scalar curvature and \(g\) is the determi