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Discrete Isothermic Surfaces in Lie Sphere Geometry

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  • © 2025

Overview

  • Provides tools that can be applied to a broad range of research areas
  • Includes highly accessible material that bridges the gap between novices and experts in the field
  • A handy introduction to the new and growing field of discrete differential geometry

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2375)

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About this book

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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Keywords

Table of contents (7 chapters)

Authors and Affiliations

  • Global Leadership School, Handong Global University, Pohang, Korea (Republic of)

    Joseph Cho

  • Faculty of Applied Information Science, Hiroshima Institute of Technology, Hiroshima, Japan

    Kosuke Naokawa

  • Department of Mathematics, Faculty of Science, Kyoto Sangyo University, Kyoto, Japan

    Yuta Ogata

  • Department of Mathematical Sciences, University of Bath, Bath, UK

    Mason Pember

  • Department of Mathematics, Kobe University, Kobe, Japan

    Wayne Rossman

  • Faculty of Science and Technology, Tokushima University, Tokushima, Japan

    Masashi Yasumoto

About the authors

Joseph Cho is a differential geometer with a primary interest in the integrable systems approach to smooth and discrete surface theory. His studies in mathematics led to a bachelor's degree from the University of California, Berkeley, a master's degree from Korea University, and a doctorate from Kobe University. He has also worked as a postdoctoral researcher at TU Wien and is currently enjoying life as an assistant professor at Handong Global University, Republic of Korea.

Kosuke Naokawa is an associate professor at Hiroshima Institute of Technology in Japan. He received his PhD from Tokyo Institute of Technology in 2013, and subsequently conducted postdoctoral research in Kobe and Vienna. His research focuses on the geometry and topology of surfaces with singularities and their discretizations.

Yuta Ogata is a researcher in the field of surface theory, integrable systems, and singularity theory. He obtained his PhD from Kobe University in 2017. After working in Okinawa, Japan, he is currently an associate professor at Kyoto Sangyo University, Japan.

Mason Pember is a lecturer of mathematics at the University of Bath, United Kingdom. He obtained his PhD from the University of Bath in 2015 and subsequently held postdocs in Kobe, Vienna and Turin. His research is in differential geometry, specialising in topics such as integrable systems, surface theory and Lie sphere geometry.

Wayne Rossman is a professor of mathematics at Kobe University, Japan. He earned his PhD from the University of Massachusetts, Amherst in 1992, and has been working ever since in the Japanese differential geometry community, interspersed with post-doctoral positions and sabbaticals in California, Brazil, Bath England, Berlin and Vienna. His expertise lies in the differential geometry of surfaces and its discretization.

Masashi Yasumoto is an associate professor at Tokushima University, Japan. He obtained his PhD from Kobe University in 2015, and subsequently conducted his research at Tübingen, Osaka, and Fukuoka as a postdoctoral researcher. His research focuses on differential and discrete differential geometry of surfaces.

Accessibility Information

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This ebook is designed with accessibility in mind, aiming to meet the ePub Accessibility 1.0 AA and WCAG 2.2 Level AA standards. It features a navigable table of contents, structured headings, and alternative text for images, ensuring smooth, intuitive navigation and comprehension. The text is reflowable and resizable, with sufficient contrast. We recognize the importance of accessibility, and we welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us at accessibilitysupport@springernature.com.

Bibliographic Information

  • Book Title: Discrete Isothermic Surfaces in Lie Sphere Geometry

  • Authors: Joseph Cho, Kosuke Naokawa, Yuta Ogata, Mason Pember, Wayne Rossman, Masashi Yasumoto

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-031-95592-1

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2025

  • Softcover ISBN: 978-3-031-95591-4Published: 10 August 2025

  • eBook ISBN: 978-3-031-95592-1Published: 08 August 2025

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XI, 238

  • Number of Illustrations: 21 b/w illustrations, 13 illustrations in colour

  • Topics: Differential Geometry, Geometry, Analysis, Global Analysis and Analysis on Manifolds

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