SURFACE FAMILY WITH COMMON LINE OF CURVATURE IN 3-DIMENSIONAL GALILEAN SPACE

Surfaces of Constant Curvature in the Pseudo-Galilean Space

We develop the local theory of surfaces immersed in the pseudo-Galilean space, a special type of Cayley-Klein spaces. We define principal, Gaussian, and mean curvatures. By this, the general setting for study of surfaces of constant curvature in the pseudo-Galilean space is provided. We describe surfaces of revolution of constant curvature. We introduce special local coordinates for surfaces of...

Surfaces of constant curvature in 3-dimensional space forms

The study of surfaces immersed in a 3-dimensional ambient space plays a central role in the theory of submanifolds. In addition, Riemannian manifolds with constant sectional curvature can be considered as the most simple examples. Thus, one can think of surfaces with constant Gauss curvature in the Euclidean space R, hyperbolic space H or 3-sphere S as very natural objects of study. Through the...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

A characterization of curves in Galilean 4-space $G_4$

‎In the present study‎, ‎we consider a regular curve in Galilean‎ ‎$4$-space $mathbb{G}_{4}$ whose position vector is written as a‎ ‎linear combination of its Frenet vectors‎. ‎We characterize such‎ ‎curves in terms of their curvature functions‎. ‎Further‎, ‎we obtain‎ ‎some results of rectifying‎, ‎constant ratio‎, ‎$T$-constant and‎ ‎$N$-constant curves in $mathbb{G}_{4}$‎.

Linear Weingarten Rotational Surfaces in Pseudo-Galilean 3-Space

In the present paper, we study rotational surfaces in the three dimensional pseudo-Galilean space G3. Also, we classify linear Weingarten rotational surfaces in G3. A linear Weingarten surface is the surface having a linear equation between the Gaussian curvature and the mean curvature of a surface. In last section, we construct isotropic rotational surfaces in G3 with prescribed mean curvature...