Surfaces with concentric or parallel $K$-contours

TL;DR

This paper characterizes and provides examples of surfaces in Euclidean 3-space that have either concentric or parallel $K$-contours, contributing to the understanding of their geometric properties.

Contribution

It introduces a formal definition of surfaces with concentric or parallel $K$-contours and offers a classification and key examples of such surfaces.

Findings

Identification of crucial examples of these surfaces

Characterization theorems for surfaces with $K$-contours

Insights into geometric properties of these surfaces

Abstract

Surfaces with concentric $K$-contours and parallel $K$-contours in Euclidean $3$-space are defined. Crucial examples are presented and characterization of them are given.