Rotational Hypersurfaces in Euclidean 4-Space with Density

Altin, Mustafa

doi:10.2339/politeknik.740513

Cited by 3 publications

(2 citation statements)

References 31 publications

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“…Furthermore, the differential geometry of different types of (hyper)surfaces in 4-D spaces has been a popular topic for geometers, recently, [17,[28][29][30][31][32][33][34][35], and etc. If Ω: U ⊂ E 3 → E 4 is a hypersurface in E 4 parametrized by: ( )…”

Section: Introductionmentioning

confidence: 99%

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Canal hypersurfaces according to one of the extended Darboux frame field in Euclidean 4-space

Kazan

2022

THERM SCI

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In the present study, we deal with canal hypersurfaces according to extended Darboux frame field of second kind in Euclidean 4-space (E4) and in this context, firstly we obtain the Gaussian, mean and principal curvatures of the canal hypersurface according to extended Darboux frame field of second kind and give some results for flatness and minimality of these hypersurfaces in E4. Also, we give some results for Weingarten canal hypersurfaces according to extended Darboux frame field of second kind in E4 and finally, we construct an example.

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Section: Introductionmentioning

confidence: 99%

“…using eqs. (29)-(31) in eq. (11), we get the canal hypersurface according to ED 2 -frame field in E 4 :…”

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Canal hypersurfaces according to one of the extended Darboux frame field in Euclidean 4-space

Kazan

2022

THERM SCI

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Rotational hypersurfaces in Lorentz-Minkowski 4-space

Altin

Kazan

2021

Hacettepe Journal of Mathematics and Statistics

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In this study, we study rotational hypersurfaces in 4-dimensional Lorentz-Minkowski space. We find the rotational hypersurfaces about spacelike axis according to Gaussian and mean curvatures in E 4 1 and give some results with the aid of the Gaussian and mean curvatures. After that, we deal with the Gauss map of rotational hypersurface about spacelike axis by obtaining the Gaussian and mean curvatures. We obtain the second and third Laplace-Beltrami operators on rotational hypersurface about spacelike axis in E 4 1 . Also, we give these characterizations for rotational hypersurfaces about timelike and lightlike axes, too.

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Rotational hypersurfaces generated by weighted mean curvature in E41 with density

Altin

2022

THERM SCI

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In this paper, we study rotational hypersurfaces in 4-D Lorentz-Minkowski space with density. We give the weighted mean curvature of a rotational hypersurface about spacelike (timelike) axis in E41 with densities ex2-y2-z2 and ex-y-z (e-y2-z2-t2 and e-y-z-t). We obtain the parametric expressions of the rotational hypersurfaces about spacelike (timelike) axis in E4 1 with density ex2-y2-z2 (e-y2-z2-t2) with respect to the weighted mean curvature and give some examples for them. Also, we give some results about rotational hypersurfaces about spacelike (timelike) axis in E41 with density ex-y-z (e-y-z-t) to be with constant or non-constant weighted mean curvature.

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Rotational Hypersurfaces in Euclidean 4-Space with Density

Abstract:  Rotational hypersurfaces in Euclidean 4-space with density have considered.  Weighted minimal and weighted flat rotational hypersurfaces in Euclidean 4-space with density have obtained.  Some examples for these hypersurfaces have constructed.

Cited by 3 publications

References 31 publications

Canal hypersurfaces according to one of the extended Darboux frame field in Euclidean 4-space

Canal hypersurfaces according to one of the extended Darboux frame field in Euclidean 4-space

Rotational hypersurfaces in Lorentz-Minkowski 4-space

Rotational hypersurfaces generated by weighted mean curvature in E41 with density

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