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FRENET EQUATIONS OF NULL CURVES

Dae Ho Jin

Open publisher page 2 citations

Abstract

The purpose of this paper is to study the geometry of null curves in a 6-dimensional semi-Riemannian manifold M_q of index q, since the general n-dimensional cases are too complicated. We show that it is possible to construct three types of Frenet equations of null curves in Mq, supported by one example. We find each types of Frenet equations invariant under any causal change. And we discuss some properties of null curves in Mq.

About this research paper

What this paper is about

The purpose of this paper is to study the geometry of null curves in a 6-dimensional semi-Riemannian manifold M_q of index q, since the general n-dimensional cases are too complicated. We show that it is possible to construct three types of Frenet equations of null curves in Mq, supported by one example. We find each types of Frenet equations invariant under any causal change. And we discuss some properties of null curves in Mq.

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OpenAlex reports 2 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

The purpose of this paper is to study the geometry of null curves in a 6-dimensional semi-Riemannian manifold M_q of index q, since the general n-dimensional cases are too complicated. We show that it is possible to construct three types of Frenet equations of null curves in Mq, supported by one example. We find each types of Frenet equations invariant under any causal change. And we discuss some properties of null curves in Mq.

Key concepts: Frenet–Serret formulas, Mathematics, Null (SQL), Mathematical analysis, Invariant (physics), Manifold (fluid mechanics), Pure mathematics, Curvature

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