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Discrete isothermic surfaces in lie sphere geometry

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Discrete isothermic surfaces in lie sphere geometryby Joseph Cho ... [et al.].
其他作者:	Cho, Joseph.
出版者:	Cham :Springer Nature Switzerland :2025.
面頁冊數:	xi, 238 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Discrete geometry.
電子資源:	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

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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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