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Laguerre minimal surfaces via congruence of lines
Author(s) -
Prado Rafaela F. do,
Roitman Pedro
Publication year - 2012
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bds013
Subject(s) - laguerre polynomials , holomorphic function , mathematics , congruence (geometry) , pure mathematics , complex plane , plane (geometry) , mathematical analysis , representation (politics) , immersion (mathematics) , harmonic function , unit sphere , minimal surface , geometry , politics , political science , law
We show how to obtain a local representation for Laguerre minimal surfaces based on vector fields in the unit two sphere that are defined in terms of a harmonic map in the complex plane. We give a geometric characterization of the Laguerre minimal surfaces constructed in the special cases where the harmonic map is either holomorphic or anti‐holomorphic.