Family of right conoid hypersurfaces with light-like axis in Minkowski four-space

Yanlin Li; Erhan Güler; Magdalena Toda; Yanlin Li; Erhan Güler; Magdalena Toda

doi:10.3934/math.2024911

AIMS Mathematics

2024, Volume 9, Issue 7: 18732-18745. doi: 10.3934/math.2024911

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Research article

Family of right conoid hypersurfaces with light-like axis in Minkowski four-space

1.
School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
2.
Key Laboratory of Cryptography of Zhejiang Province, Hangzhou Normal University, Hangzhou 311121, China
3.
Department of Mathematics, Faculty of Sciences, Bartın University, Kutlubey Campus, 74100 Bartın, Turkey
4.
Department of Mathematics and Statistics, Texas Tech University, Lubbock TX 79409-1042, USA

Received: 08 April 2024 Accepted: 29 May 2024 Published: 04 June 2024
MSC : 53A35, 53C42

In the realm of the four-dimensional Minkowski space $ \mathbb{L}^{4} $, the focus is on hypersurfaces classified as right conoids and defined by light-like axes. Matrices associated with the fundamental form, Gauss map, and shape operator, all specifically tailored for these hypersurfaces, are currently undergoing computation. The intrinsic curvatures of these hypersurfaces are determined using the Cayley-Hamilton theorem. The conditions of minimality are addressed by the analysis. The Laplace-Beltrami operator for such hypersurfaces is computed, accompanied by illustrative examples aimed at fostering a more profound understanding of the involved mathematical principles. Additionally, scrutiny is applied to the umbilical condition, and the introduction of the Willmore functional for these hypersurfaces is presented.
- Minkowski four-space,
- right conoid hypersurface family,
- light-like axis,
- Gauss map,
- Willmore functional
Citation: Yanlin Li, Erhan Güler, Magdalena Toda. Family of right conoid hypersurfaces with light-like axis in Minkowski four-space[J]. AIMS Mathematics, 2024, 9(7): 18732-18745. doi: 10.3934/math.2024911

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Abstract

In the realm of the four-dimensional Minkowski space $ \mathbb{L}^{4} $, the focus is on hypersurfaces classified as right conoids and defined by light-like axes. Matrices associated with the fundamental form, Gauss map, and shape operator, all specifically tailored for these hypersurfaces, are currently undergoing computation. The intrinsic curvatures of these hypersurfaces are determined using the Cayley-Hamilton theorem. The conditions of minimality are addressed by the analysis. The Laplace-Beltrami operator for such hypersurfaces is computed, accompanied by illustrative examples aimed at fostering a more profound understanding of the involved mathematical principles. Additionally, scrutiny is applied to the umbilical condition, and the introduction of the Willmore functional for these hypersurfaces is presented.

References

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