Translation hypersurfaces of semi-Euclidean spaces with constant scalar curvature

Derya Sağlam; Cumali Sunar; Derya Sağlam; Cumali Sunar

doi:10.3934/math.2023252

AIMS Mathematics

2023, Volume 8, Issue 2: 5036-5048. doi: 10.3934/math.2023252

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Translation hypersurfaces of semi-Euclidean spaces with constant scalar curvature

Derya Sağlam ^,,
Cumali Sunar

Kırıkkale University, Faculty of Art and Science, Department of Mathematics, Turkey

Received: 08 July 2022 Revised: 19 November 2022 Accepted: 21 November 2022 Published: 12 December 2022
MSC : 53A04, 53A25, 53A40

In this paper, we present translation hypersurfaces of semi-Euclidean spaces with zero scalar curvature. In addition, we prove that translation hypersurfaces with constant scalar curvature must have zero scalar curvature in the semi-Euclidean space $ \mathbb{R}_{q}^{n+1} $ for $ n\geq 3 $.
- translation hypersurfaces,
- scalar curvature,
- semi-Euclidean space
Citation: Derya Sağlam, Cumali Sunar. Translation hypersurfaces of semi-Euclidean spaces with constant scalar curvature[J]. AIMS Mathematics, 2023, 8(2): 5036-5048. doi: 10.3934/math.2023252

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Abstract

In this paper, we present translation hypersurfaces of semi-Euclidean spaces with zero scalar curvature. In addition, we prove that translation hypersurfaces with constant scalar curvature must have zero scalar curvature in the semi-Euclidean space $ \mathbb{R}_{q}^{n+1} $ for $ n\geq 3 $.

References

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