Aydin, Muhittin Evren Constant curvature surfaces in a pseudo-isotropic space. (English) Zbl 1405.53015 Tamkang J. Math. 49, No. 3, 221-233 (2018). Summary: In this study, we deal with the local structure of curves and surfaces immersed in a pseudo-isotropic space \(\mathbb{I}^3_p\) that is a particular Cayley-Klein space. We provide the formulas of curvature, torsion and Frenet trihedron for spacelike and timelike curves, respectively. The causal character of all admissible surfaces in \(\mathbb{I}^3_p\) has to be timelike up to its absolute. We introduce the formulas of Gaussian and mean curvature for timelike surfaces in \(\mathbb{I}^3_p\). As applications, we describe the surfaces of revolution which are the orbits of a plane curve under a hyperbolic rotation with constant Gaussian and mean curvature. Cited in 3 Documents MSC: 53A35 Non-Euclidean differential geometry 53B25 Local submanifolds 53B30 Local differential geometry of Lorentz metrics, indefinite metrics 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) Keywords:pseudo-isotropic space; surface of revolution; Gaussian curvature; mean curvature PDFBibTeX XMLCite \textit{M. E. Aydin}, Tamkang J. Math. 49, No. 3, 221--233 (2018; Zbl 1405.53015) Full Text: DOI arXiv