On Inverse Surfaces in Euclidean 3-Space

TL;DR

This paper investigates inverse surfaces in Euclidean 3-space, establishing relationships between their geometric properties such as Christoffel symbols, curvatures, shape operators, and fundamental forms.

Contribution

It provides new theoretical results linking various differential geometric quantities of inverse surfaces in three-dimensional Euclidean space.

Findings

Derived relations between Christoffel symbols and inverse surface properties

Established connections between normal curvatures and shape operators for inverse surfaces

Analyzed the third fundamental form in the context of inverse surface geometry

Abstract

In this paper, we study the inverse surfaces in 3-dimensional Euclidean space $\mathbb{E}^{3}$. We obtain some results relating Christoffel symbols, the normal curvatures, the shape operators and the third fundamental forms of the inverse surfaces