L-minimal canal surfaces

Abstract

By the method of moving frames we provide an explicit, elementary description of the enveloping surfaces of a 1-parameter family of oriented spheres that are extremals of the variational problem defined on immersed surfaces in Euclidean space by the functional (f,S) → , (H2 − K)K−1dA (L-minimal canal surfaces).

Keywords

• laguerre geometry
• legendre surfaces
• l-minimal canal surfaces