Geometric properties of hypersurfaces in the geometry of Thurston Nil 4

Abstract

In this research we give some geometric properties of hypersurfaces (M3; g) in the nilpotent Lie group (Nil4; eg). First, we give a left invariant metric, the Levi-Civita connection, Riemannian curvature, and the Ricci tensor in an orthonormal basis of vector eld in Nil4, beside, we note a classi cation of Codazzi hypersurfaces in a Lie group (Nil4; eg). We also give a characterization of a class of minimal hypersurfaces in (Nil4; eg) with an example of a minimal surface in this class.