2018/02/15 by Emilio Musso, Lorenzo Nicolodi · 3 citations
Mathematics · #math.DG #msc:53A35 #msc:53C42
paper · pdf · doi:10.4064/bc117-8
published in Banach Center Publications 117, 223-255 (Institute of Mathematics, Polish Academy of Sciences) · 32 pages. To appear in Banach Center Publications, special volume "Geometry of Lagrangian Grassmannians and nonlinear PDEs" (J. Gutt, G. Manno and G. Moreno, eds.). arXiv admin note: text overlap with arXiv:1401.1776
arxiv created 2018/02/15 · crossref issued 2019/01/01 · crossref published 2019/01/01 · crossref published-online 2019/01/01 · crossref created 2019/02/22 · crossref deposited 2019/02/22 · arxiv updated 2019/03/01 · crossref indexed 2026/08/05
This exposition gives an introduction to the theory of surfaces in Laguerre geometry and surveys some results, mostly obtained by the authors, about 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. As an example, the Cartan-Kaehler theorem is applied to study the Cauchy problem for the Pfaffian differential system of L-minimal surfaces. This is an elaboration of the talks given by the authors at IMPAN, Warsaw, in September 2016. The objective was to illustrate, by the subject of Laguerre surface geometry, some of the topics presented in a series of lectures held at IMPAN by G. R. Jensen on Lie sphere geometry and by B. McKay on exterior differential systems.