Spinor Frenet Equations in Three Dimensional Lie Groups

TL;DR

This paper explores the formulation of spinor Frenet equations within three-dimensional Lie groups equipped with a bi-invariant metric, extending classical differential geometry to more complex algebraic structures.

Contribution

It introduces spinor Frenet equations in three-dimensional Lie groups and derives specific cases for particular types of these groups, advancing geometric analysis in algebraic contexts.

Findings

Derived spinor Frenet equations for general three-dimensional Lie groups

Obtained explicit forms for special cases of Lie groups

Extended classical differential geometry to Lie group settings

Abstract

In this paper, we study spinor Frenet equations in three dimensional Lie Groups with a bi-invariant metric. Also, we obtain spinor Frenet equations for special cases of three dimensional Lie groups.