On Geometry of Lorentzian Immersions with non-null Hyperelastic Curves

Abstract

We characterize Lorentzian submanifolds by using non-null hyperelastic curvesalong a Lorentzian immersion defined between suitable two Lorentzianmanifolds. We introduce a Lorentzian hyperelastic immersion as amap that carries a hyperelastic curve in the submanifold to ahyperelastic curve in the ambient manifold by the isometric immersion. Then,we investigate the characterization of submanifolds by using hyperelastic curvesalong Lorentzian immersions. Also, we exemplify the findings.