On the new approach for the energy of elastica - Körpınar, Talat; Demirkol, Rıdvan Cem (UNIV ESTADUAL MARINGA, PRO-REITORIA PESQUISA POS-GRADUACAO, 2018)
In this work, we firstly describe conditions for being elastica in Minkowski space E-1(4). Then we investigate the energy of the elastic curves and exploit its relationship with the energy of Bishop vectors belong to that elastic curves E-1(4). Finally, we characterize non-elastic curves in E-1(4) and compute their energy to see the distinction between energies for the curves of elastic and non-elastic case in Minkowski space E-1(4).
Keywords: energy; Minkowski space; elastic curves; parallel vector fields