Laguerre minimal surfaces via congruence of lines | Zendy

Prado Rafaela F. do | Zendy; Roitman Pedro | Zendy

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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.

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