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

• Autorzy: Kuşak Samanci Hatice , Ayaz Sedat , Kocayiğit Hüseyin

Identyfikatory

DOI

10.2478/fcds-2021-0016

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Laplace operator; harmonic 1-type curve; N-Bishop frame; harmonic curves

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Foundations of Computing and Decision Sciences
• Rocznik: 2021
• Tom: Vol. 46, No. 3
• Strony: 235--254
• Opis fizyczny: Bibliogr. 30 poz., rys.

Twórcy

autor

Kuşak Samanci Hatice

• Bitlis Eren Un. Dep. of Math.

autor

Ayaz Sedat

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

autor

Kocayiğit Hüseyin

• Celal Bayar Un. Dep. of Math

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).