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Discrete isothermic surfaces in lie sphere geometry

Record Type:	Electronic resources : Monograph/item
Title/Author:	Discrete isothermic surfaces in lie sphere geometryby Joseph Cho ... [et al.].
other author:	Cho, Joseph.
Published:	Cham :Springer Nature Switzerland :2025.
Description:	xi, 238 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Discrete geometry.
Online resource:	https://doi.org/10.1007/978-3-031-95592-1
ISBN:	9783031955921$q(electronic bk.)

Discrete isothermic surfaces in lie sphere geometry
Discrete isothermic surfaces in lie sphere geometry[electronic resource] /by Joseph Cho ... [et al.]. - Cham :Springer Nature Switzerland :2025. - xi, 238 p. :ill. (some col.), digital ;24 cm. - Lecture notes in mathematics,v. 23751617-9692 ;. - Lecture notes in mathematics ;2035..

Chapter 1. Introduction -- Chapter 2.Isothermic surfaces in Möbius geometry -- Chapter 3. From smooth to discrete via permutability -- Chapter 4. Discrete Isothermic surfaces -- Chapter 5. Ω-surfaces in Lie sphere geometry -- Chapter 6. Integrability of Ω-surfaces via isothermicity -- Chapter 7. Discrete Ω-surfaces.

This book provides a highly accessible approach to discrete surface theory, within the unifying frameworks of Moebius and Lie sphere geometries, from the perspective of transformation theory of surfaces rooted in integrable systems. It elucidates how the transformation theory for smooth surfaces can be used as a springboard for understanding the discretization process of certain types of surfaces, and it is aimed at high-level undergraduate students, graduate students and professional mathematicians alike. The reader will benefit from the detailed exploration of the transformation theory of surfaces, including Christoffel, Calapso and Darboux transformations of particular classes of surfaces, as well as becoming more familiar with integrable systems via zero curvature representation, including flat connections and conserved quantities, in both smooth and discrete settings.

ISBN: 9783031955921$q(electronic bk.)

Standard No.: 10.1007/978-3-031-95592-1doiSubjects--Topical Terms:

277229
Discrete geometry.

LC Class. No.: QA640.7

Dewey Class. No.: 516.11

Discrete isothermic surfaces in lie sphere geometry
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505 0 $a Chapter 1. Introduction -- Chapter 2.Isothermic surfaces in Möbius geometry -- Chapter 3. From smooth to discrete via permutability -- Chapter 4. Discrete Isothermic surfaces -- Chapter 5. Ω-surfaces in Lie sphere geometry -- Chapter 6. Integrability of Ω-surfaces via isothermicity -- Chapter 7. Discrete Ω-surfaces.
520 $a This book provides a highly accessible approach to discrete surface theory, within the unifying frameworks of Moebius and Lie sphere geometries, from the perspective of transformation theory of surfaces rooted in integrable systems. It elucidates how the transformation theory for smooth surfaces can be used as a springboard for understanding the discretization process of certain types of surfaces, and it is aimed at high-level undergraduate students, graduate students and professional mathematicians alike. The reader will benefit from the detailed exploration of the transformation theory of surfaces, including Christoffel, Calapso and Darboux transformations of particular classes of surfaces, as well as becoming more familiar with integrable systems via zero curvature representation, including flat connections and conserved quantities, in both smooth and discrete settings.
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650 0 $a Geometry, Differential. $3 182610
650 1 4 $a Differential Geometry. $3 273785
650 2 4 $a Geometry. $3 183883
650 2 4 $a Differential Equations. $3 285983
650 2 4 $a Global Analysis and Analysis on Manifolds. $3 273786
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