Weingarten and Linear Weingarten Canal Surfaces

TL;DR

This paper explores specific classes of canal surfaces in three-dimensional space characterized by linear and Weingarten relations among their curvature functions, expanding the understanding of their geometric properties.

Contribution

It introduces and analyzes new classes of Weingarten and linear Weingarten canal surfaces in IR^3, focusing on their curvature relations.

Findings

Characterization of (K,H), (K,K_{II}), (H,K_{II})-Weingarten canal surfaces

Analysis of (K,H), (K,K_{II}), (H,K_{II}) and (K,H,K_{II})-linear Weingarten canal surfaces

Identification of geometric properties related to curvature relations

Abstract

In this study, we investigated the (K,H), (K,K_{II}), (H,K_{II})-Weingarten and (K,H),(K,K_{II}),(H,K_{II}) and (K,H,K_{II})-linear Weingarten canal surfaces in IR^3.