Premium
The Conformal Arclength Functional
Author(s) -
Musso Emilio
Publication year - 1994
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19941650109
Subject(s) - conformal map , mathematics , invariant (physics) , euler's formula , space (punctuation) , extremal length , mathematical analysis , conformal symmetry , mathematical physics , computer science , operating system
A generic smooth curve of the three dimensional Möbius space admits a natural parameter (or conformal arclength). Integrating the conformal arclength we get a conformally invariant variational problem. In the present paper we study the extremal curves of this variational problem. We derive the associated Euler‐Lagrange equations and we get the natural equations of the extremal curves. The natural equations are integrated and the explicit solutions are given.