Métricas Riemannianas en k Superficies de R^n, Un Acercamiento a Grupos de Heisenberg

Abstract

The following work seeks to study geometry in Heisenberg groups. A Heisenberg group of dimension three, noted as H3 is a subgroup of the group GL (3; R) denoting the group of three-order and invertible square matrices. Since all Lie algebra of dimension n can be represented within the square matrix algebra of order n × n, we will see that H3 is a closed subgroup of GL (3; R) and with the properties of Lie groups will be provided with a Metric invariant to the left that in turn will allow to deduce the fundamental forms, geodesics and normal functions in hypersurfaces. At the end a brief introduction to minimal surfaces in H3 is given with some examples.