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.
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.
Examines each of these parameters in crucial depth and makes the argument that life forms we would recognize may be more common in our solar system than many assume. Considers exotic forms of life that would not have to rely on carbon as the basic chemical element, solar energy as the main energy source, or water as the primary solvent and the question of detecting bio- and geosignatures of such life forms, ranging from earth environments to deep space. Seeks an operational definition of life and investigate the realm of possibilities that nature offers to realize this very special state of matter. Avoids scientific jargon wherever possible to make this intrinsically interdisciplinary subject understandable to a broad range of readers.
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