Classification of Codazzi and Note on Minimal Hypersurfaces in $Nil^{4}$

Year 2023, , 707 - 714, 29.10.2023

Noura Djellalı Abdelbasset Hasni Ahmed Mohammed Cherif Mohamed Belkhelfa

https://doi.org/10.36890/iejg.1256112

Cited By: 2

Abstract

In this paper, we give a classification of Codazzi hypersurfaces in a Lie group $(Nil^{4},\widetilde g)$. We also give a characterization of a class of minimal hypersurfaces in $(Nil^{4},\widetilde g)$ with an example of a minimal surface in this class.

Keywords

Codazzi hypersurfaces, minimal hypersurfaces., nilpotent Lie group

References

• [1] Belkhelfa M., Dillen F., Inoguchi J.: Surfaces with parallel second fundamental form in Bianchi-Cartan-Vranceanu spaces. Banach Center Publishing, 57, 67-87 (2002).
• [2] Calvaruso G., De Leo B.: Curvature properties of four-dimensional generalized symmetric spaces. J. Geom. 90, 30-46 (2008).
• [3] Filipkiewicz R.: Four dimensional geometries. PhD thesis, University of Warwick, Great Britain (1983).
• [4] Hasni A.: Les géométries de Thurston et la pseudo symétrie d’après R. Deszcz. PhD thesis, University of Tlemcen, Algeria (2014).
• [5] Lawson H.B.: Local rigidity theorems for minimal hypersurfaces. Ann. Math. 89, 187-197 (1969).
• [6] Leo B.D., Veken J.V.: Totally geodesic hypersurfaces of four-dimensional generalized symmetric spaces. Geom Dedicata, 159, 373-387 (2012).
• [7] O’Neil: Semi-Riemannian Geometry. Academic Press, New York (1983).
• [8] Willmore T.J.: Riemannian Geometry. Clarendon Press, New York (1993).