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

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dc.contributor.authorSamanci H.K.
dc.contributor.authorAyaz S.
dc.contributor.authorKocayiǧit H.
dc.date.accessioned2024-07-22T08:05:43Z
dc.date.available2024-07-22T08:05:43Z
dc.date.issued2021
dc.description.abstractA 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. © 2021 Hatice Kuşak Samanci et al., published by Sciendo.
dc.identifier.DOI-ID10.2478/fcds-2021-0016
dc.identifier.issn08676356
dc.identifier.urihttp://akademikarsiv.cbu.edu.tr:4000/handle/123456789/13238
dc.language.isoEnglish
dc.publisherSciendo
dc.rightsAll Open Access; Gold Open Access
dc.subjectDifferential equations
dc.subjectFlow of fluids
dc.subjectGeometry
dc.subjectLaplace transforms
dc.subjectQuantum theory
dc.subjectVector spaces
dc.subjectWave propagation
dc.subjectDiffusion equations
dc.subjectEngineering science
dc.subjectEuclidean
dc.subjectHarmonic 1-type curve
dc.subjectHarmonic curves
dc.subjectHeat-flow
dc.subjectLaplace operator
dc.subjectN-bishop frame
dc.subjectSpace curve
dc.subjectType curves
dc.subjectHarmonic analysis
dc.titleSome New Characterizations of the Harmonic and Harmonic 1-Type Curves in Euclidean 3-Space
dc.typeArticle

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