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Surfaces in Laguerre geometry

Volume 117 / 2019

Emilio Musso, Lorenzo Nicolodi Banach Center Publications 117 (2019), 223-255 MSC: Primary 53A35; Secondary 53C42. DOI: 10.4064/bc117-8

Abstract

This exposition gives an introduction to the theory of surfaces in Laguerre geometry and surveys some significant results concerning three important classes of surfaces in Laguerre geometry, namely $L$-isothermic, $L$-minimal, and generalized $L$-minimal surfaces. The quadric model of Lie sphere geometry is adopted for Laguerre geometry and the method of moving frames is used throughout. The Cartan–Kähler theorem for exterior differential systems is applied to study the Cauchy problem for the Pfaffian differential system of $L$-minimal surfaces. This paper is an elaboration of our talks at the IMPAN Workshop in Warsaw. Our objective was to illustrate, by the subject of Laguerre surface geometry, some of the main concepts presented in the lecture series by G. R. Jensen on Lie sphere geometry and by B. McKay on exterior differential systems.

Authors

  • Emilio MussoDipartimento di Scienze Matematiche
    Politecnico di Torino
    Corso Duca degli Abruzzi 24
    I-10129 Torino, Italy
    e-mail
  • Lorenzo NicolodiDipartimento di Scienze Matematiche, Fisiche e Informatiche
    Università di Parma
    Parco Area delle Scienze 53/A
    I-43124 Parma, Italy
    e-mail

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