Gauss-Bonnet theorem in Lorentzian Sasakian space forms

Haiming Liu; Jiajing Miao; Haiming Liu; Jiajing Miao

doi:10.3934/math.2021509

AIMS Mathematics

2021, Volume 6, Issue 8: 8772-8791. doi: 10.3934/math.2021509

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Research article

Gauss-Bonnet theorem in Lorentzian Sasakian space forms

Haiming Liu ,
Jiajing Miao ^,

School of Mathematics, Mudanjiang Normal University, Mudanjiang 157011, China

Received: 11 March 2021 Accepted: 03 June 2021 Published: 10 June 2021
MSC : 53C40, 53C42

In this paper, we use a Lorentzian approximation scheme to compute the sub-Lorentzian limit of curvatures for curves and Lorentzian surfaces in the Lorentzian Bianci-Cartan-Vranceanu model of $ 3 $-dimensional Lorentzian Sasakian space forms. Based on these results, we get a Gauss-Bonnet theorem in the Lorentzian Sasakian space forms.
- Lorentzian Sasakian space forms,
- Gauss-Bonnet theorem,
- Lorentzian approximation scheme,
- sub-Riemannian geometry,
- curvature
Citation: Haiming Liu, Jiajing Miao. Gauss-Bonnet theorem in Lorentzian Sasakian space forms[J]. AIMS Mathematics, 2021, 6(8): 8772-8791. doi: 10.3934/math.2021509

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Abstract

In this paper, we use a Lorentzian approximation scheme to compute the sub-Lorentzian limit of curvatures for curves and Lorentzian surfaces in the Lorentzian Bianci-Cartan-Vranceanu model of $ 3 $-dimensional Lorentzian Sasakian space forms. Based on these results, we get a Gauss-Bonnet theorem in the Lorentzian Sasakian space forms.

References

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