Year: 1997
Type: preprint
Abstract: We describe here a general method for finding symmetries of minimal surfaces in R 3 , namely transformations sending a minimal immersion to another minimal immersion. More specifically we will be looking for infinitesimal symmetries, i.e. vector fields tangent to a Lie group acting on the set of minimal surfaces. Using Noether's theorem, we derive conserved quantities, i.e. cohomology classes on H 1 , that permit us to write so called balancing formulas. Some examples of applications of such balancing formulas are quoted below. Others may be found in [6]. 1 Jet bundles and differential equations We follow the formalism in [5] transposed in the fiber bundle setting. Though we are mostly interested in maps from a surface M to R 3 , we will write them as sections of the trivial bundle M \\Theta R 3 . This method follows the more general construction (see [9]) and explains the type of vector fields and transformations we will encounter. 1.1 Jet bundles and prolongation Let N be a tr...
Source: HAL
Authors: Pascal Romon Universit'e, Pascal Romon, Fiber F
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7097605524