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–K ̈ahler theorem for exterior di erential systems is applied to study the Cauchy problem for the Pfa an di erential 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 di erential systems.

Surfaces in Laguerre Geometry / Musso, Emilio. - STAMPA. - 117:(2019), pp. 223-255. (Intervento presentato al convegno Workshop on Geometry of Lagrangian Grassmannians and Nonlinear PDEs, tenutosi a Banach Centre in Warsaw nel September 5–9, 2016) [10.4064/bc117-8].

Surfaces in Laguerre Geometry

Emilio Musso
2019

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–K ̈ahler theorem for exterior di erential systems is applied to study the Cauchy problem for the Pfa an di erential 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 di erential systems.
2019
978-83-86806-43-0
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2727570
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