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Pseudo-Isotropic Lorentzian Centroaffine Hypersurfaces 2

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Abstract

In this paper, we classify locally 2 and 3 dimensional pseudo-isotropic Lorentzian centroaffine hypersurfaces with vanishing \(K^2\).

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References

  1. Birembaux, O.: Pseudo-isotropic centro-affine Lorentzian surfaces. Mathematics 8(8), 1284 (2020)

    Article  Google Scholar 

  2. Birembaux, O., Cao, L.: Pseudo-isotropic Lorentzian centroaffine hypersurfaces-1. Results Math. 77(24), 1–30 (2022)

    MathSciNet  MATH  Google Scholar 

  3. Birembaux, O., Cao, L.: Lightlike pseudo-isotropic centroaffine Lorentzian hypersurfaces of dimension 3. Preprint

  4. Birembaux, O., Djorić, M.: Isotropic affine spheres. Acta Math. Sin. (Engl. Ser.) 28, 1955–1972 (2012)

    Article  MathSciNet  Google Scholar 

  5. Birembaux, O., Vrancken, L.: Isotropic affine hypersurfaces of dimension 5. J. Math. Anal. Appl. 417, 918–962 (2014)

    Article  MathSciNet  Google Scholar 

  6. Chen, B.Y.: Differential Geometry of Warped Product Manifolds and Submanifolds. World Scientific Publishing Co., Singapore (2017)

    Book  Google Scholar 

  7. Cheng, X.X., Hu, Z.J.: Classification of locally strongly convex isotropic centroaffine hypersurfaces. Differ. Geom. Appl. 65, 30–54 (2019)

    Article  MathSciNet  Google Scholar 

  8. Cabrerizo, J.L., Fernández, M., Gómez, J.S.: Rigidity of pseudo-isotropic immersions. J. Geom. Phys. 59, 834–842 (2009)

    Article  MathSciNet  Google Scholar 

  9. Dillen, F., Magid, M., Vrancken, L.: Affine hyperspheres with constant affine sectional curvature. In: Geometry and Topology of Submanifolds X , pp. 31–53 (2000)

  10. Li, A.M., Simon, U., Zhao, G.: Global Affine Differential Geometry of Hypersurfaces. Walter de Gruyter, Berlin (1993)

    Book  Google Scholar 

  11. Moruz, M., Vrancken, L.: A classification of isotropic affine hyperspheres. Int. J. Math. 27, 1650074 (2016)

    Article  MathSciNet  Google Scholar 

  12. Nomizu, K., Sasaki, T.: Affine Differential Geometry, Geometry of Affine Immersions. Cambridge University Press, Cambridge (1994)

    MATH  Google Scholar 

  13. O’Neill, B.: Isotropic and Kähler immersions. Can. J. Math. 17, 907–915 (1965)

    Article  Google Scholar 

  14. O’Neill, B.: Semi-Riemannian Geometry with Application to Relativity. Academic Press, Boca Raton (1983)

    MATH  Google Scholar 

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Acknowledgements

The authors express great thanks to Professor Luc Vrancken for various helps in this paper. Lin Cao is supported by grant of NSFC No. 11901250 and CSC.

Funding

Lin Cao is supported by grant of NSFC No. 11901250 and CSC.

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Authors and Affiliations

  1. LMI, Université polytechnique Hauts-de-France, 59313, Valenciennes Cedex 9, France

    Olivier Birembaux

  2. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, China

    Lin Cao

  3. Departement Wiskunde, Katholieke Universiteit Leuven, 3001, Leuven, Belgium

    Lin Cao

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  1. Olivier Birembaux
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  2. Lin Cao
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Correspondence to Lin Cao.

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Birembaux, O., Cao, L. Pseudo-Isotropic Lorentzian Centroaffine Hypersurfaces 2. Results Math 77, 179 (2022). https://doi.org/10.1007/s00025-022-01721-5

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