An approach to energy and elastic for curves with extended Darboux frame in Minkowski space

Talat Körpinar; Yasin Ünlütürk; Talat Körpinar; Yasin Ünlütürk

doi:10.3934/math.2020071

AIMS Mathematics

2020, Volume 5, Issue 2: 1025-1034. doi: 10.3934/math.2020071

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Research article

An approach to energy and elastic for curves with extended Darboux frame in Minkowski space

Talat Körpinar ^{1
,
,},
Yasin Ünlütürk ²

1.
Mus Alparslan University, Department of Mathematics, 49250, Muş/Turkiye
2.
Kırklareli University, Department of Mathematics, 39100 Kırklareli/Turkiye

Received: 20 November 2019 Accepted: 03 January 2020 Published: 09 January 2020
MSC : 53A04

In this paper, we construct the energy for the ED-frame field of the first and second kind on an orientable hypersurface in Minkowski space. We obtain the geometric properties of some graphics by way of energy. We apply totally diverse discussion and approach to illustrate bending energy functional for the ED-frame field of the first and second kind. Finally, we have a new relation for angle and energy of the curve on an orientable hypersurface in Minkowski space.
- energy,
- ED-frame field,
- hypersurface,
- vector fields,
- bending energy
Citation: Talat Körpinar, Yasin Ünlütürk. An approach to energy and elastic for curves with extended Darboux frame in Minkowski space[J]. AIMS Mathematics, 2020, 5(2): 1025-1034. doi: 10.3934/math.2020071

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Abstract

In this paper, we construct the energy for the ED-frame field of the first and second kind on an orientable hypersurface in Minkowski space. We obtain the geometric properties of some graphics by way of energy. We apply totally diverse discussion and approach to illustrate bending energy functional for the ED-frame field of the first and second kind. Finally, we have a new relation for angle and energy of the curve on an orientable hypersurface in Minkowski space.

References

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