Rotational surfaces in a $3$-dimensional normed space

TL;DR

This paper investigates rotational surfaces with constant Minkowski curvature in a 3D normed space, generalizing classical surfaces like catenoids and Delaunay surfaces within this geometric framework.

Contribution

It introduces a generalization of classical rotational surfaces such as catenoids and Delaunay surfaces in a 3D normed space with rotational symmetry.

Findings

Characterization of rotational surfaces with constant Minkowski Gaussian curvature

Construction of surfaces with constant Minkowski mean curvature

Extension of classical surfaces to a Minkowski normed space context

Abstract

We study rotational surfaces with constant Minkowski Gaussian curvature and rotational surfaces with constant Minkowski mean curvature in a $3$-dimensional normed space with rotationally symmetric norm. We have a generalization of the catenoid, pseudo-sphere and Delaunay surfaces.