Homothetical surfaces in three dimensional psuedo-Galilean space

Abstract

A homothetical surface arises as a graph of a function $z={\phi }_1(v_1){\phi }_2(v_2)$. In this paper, we study the homothetical surfaces in three dimensional psuedo-Galilean space$\left({\mathbb{G}}_3^1\right)$ satisfying the conditions ${\Delta }^{II}{\text{x}}_i={\lambda }_i{\text{x}}_i,$ where ${\Delta }^{II}$ is the Laplacian with respect to second fundamental form. In particular, we show the non-existence of any such type of surface in ${\mathbb{G}}_3^1.$

arXiv commentAccepted in Advances in Applied Clifford Algebras, Springer

References in corpus (1)

• Non-zero constant curvature factorable surfaces in pseudo-Galilean space