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
Surfaces in Conformal Geometry
β Scribed by T. J. Willmore
- Book ID
- 110240122
- Publisher
- Springer
- Year
- 2000
- Tongue
- English
- Weight
- 81 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0232-704X
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π SIMILAR VOLUMES
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.
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