Smarandache Ruled Surfaces According to Bishop Frame in E3

TL;DR

This paper introduces new Smarandache ruled surfaces based on Bishop frames in three-dimensional space, analyzing their fundamental forms and curvatures to explore their geometric properties.

Contribution

It presents novel Smarandache ruled surfaces constructed via Bishop frames, expanding the understanding of their geometric characteristics.

Findings

Fundamental forms and curvatures of the new surfaces are derived.

Characteristics of the surfaces are analyzed and illustrated with an example.

Abstract

This paper introduces new ruled surfaces according to Bishop frame by referring to the main idea of Smarandache geometry. The fundamental forms and the corresponding curvatures are provided to put forth some characteristics of each surface. Finally, an example is given to illustrate the constructed surfaces.