TY - JOUR T1 - Classification of Codazzi and Note on Minimal Hypersurfaces in $Nil^{4}$ AU - Mohammed Cherif, Ahmed AU - Djellalı, Noura AU - Hasni, Abdelbasset AU - Belkhelfa, Mohamed PY - 2023 DA - October Y2 - 2023 DO - 10.36890/iejg.1256112 JF - International Electronic Journal of Geometry JO - Int. Electron. J. Geom. PB - Kazım İlarslan WT - DergiPark SN - 1307-5624 SP - 707 EP - 714 VL - 16 IS - 2 LA - en AB - 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. KW - Codazzi hypersurfaces KW - minimal hypersurfaces. KW - nilpotent Lie group CR - [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). CR - [2] Calvaruso G., De Leo B.: Curvature properties of four-dimensional generalized symmetric spaces. J. Geom. 90, 30-46 (2008). CR - [3] Filipkiewicz R.: Four dimensional geometries. PhD thesis, University of Warwick, Great Britain (1983). CR - [4] Hasni A.: Les géométries de Thurston et la pseudo symétrie d’après R. Deszcz. PhD thesis, University of Tlemcen, Algeria (2014). CR - [5] Lawson H.B.: Local rigidity theorems for minimal hypersurfaces. Ann. Math. 89, 187-197 (1969). CR - [6] Leo B.D., Veken J.V.: Totally geodesic hypersurfaces of four-dimensional generalized symmetric spaces. Geom Dedicata, 159, 373-387 (2012). CR - [7] O’Neil: Semi-Riemannian Geometry. Academic Press, New York (1983). CR - [8] Willmore T.J.: Riemannian Geometry. Clarendon Press, New York (1993). UR - https://doi.org/10.36890/iejg.1256112 L1 - https://dergipark.org.tr/en/download/article-file/2973184 ER -