<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>A Laplace operator and harmonic curve have very important uses in various engineering science such as quantum mechanics, wave propagation, diffusion equation for heat, and fluid flow. Additionally, the differential equation characterizations of the harmonic curves play an important role in estimating the geometric properties of these curves. Hence, this paper proposes to compute some new differential equation characterizations of the harmonic curves in Euclidean 3-space by using an alternative frame named the N-Bishop frame. Firstly, we investigated some new differential equation characterizations of the space curves due to the N-Bishop frame. Secondly, we firstly introduced some new space curves which have the harmonic and harmonic 1-type vectors due to alternative frame N-Bishop frame. Finally, we compute new differential equation characterizations using the N-Bishop Darboux and normal Darboux vectors. Thus, using these differential equation characterizations we have proved in which conditions the curve indicates a helix.</p>
</abstract>

A Laplace operator and harmonic curve have very important uses in various engineering science such as quantum mechanics, wave propagation, diffusion equation for heat, and fluid flow. Additionally, the differential equation characterizations of the harmonic curves play an important role in estimating the geometric properties of these curves. Hence, this paper proposes to compute some new differential equation characterizations of the harmonic curves in Euclidean 3-space by using an alternative frame named the N-Bishop frame. Firstly, we investigated some new differential equation characterizations of the space curves due to the N-Bishop frame. Secondly, we firstly introduced some new space curves which have the harmonic and harmonic 1-type vectors due to alternative frame N-Bishop frame. Finally, we compute new differential equation characterizations using the N-Bishop Darboux and normal Darboux vectors. Thus, using these differential equation characterizations we have proved in which conditions the curve indicates a helix.

Some New Characterizations of The Harmonic and Harmonic 1-Type Curves in Euclidean 3-Space

Bitlis Eren Un. Dep. of Math. (Master Std.)

Foundations of Computing and Decision Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

A Laplace operator and harmonic curve have very important uses in various engineering science such as quantum mechanics, wave propagation, diffusion equation...

Some New Characterizations of The Harmonic and Harmonic 1-Type Curves in Euclidean 3-Space

Published Online: Sep 17, 2021

Page range: 235 - 254

Received: Apr 09, 2020

Accepted: Mar 01, 2021

DOI: https://doi.org/10.2478/fcds-2021-0016

Keywords
Laplace operator, harmonic curve, harmonic 1-type curve, N-Bishop frame

© 2021 Hatice Kuşak Samanci et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Some New Characterizations of The Harmonic and Harmonic 1-Type Curves in Euclidean 3-Space

Published Online: Sep 17, 2021

Page range: 235 - 254

Received: Apr 09, 2020

Accepted: Mar 01, 2021

DOI: https://doi.org/10.2478/fcds-2021-0016

KeywordsLaplace operator, harmonic curve, harmonic 1-type curve, N-Bishop frame

© 2021 Hatice Kuşak Samanci et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Laplace operator, harmonic curve, harmonic 1-type curve, N-Bishop frame