Spacelike immersions in certain Lorentzian manifolds with lightlike foliations (Q6645880)

Generalized Schwarzschild spacetimes are \((m+2)\)-dimensional Lorentzian manifolds defined as warped products with base given by an open subset of \(\mathbb{R}^2\) endowed with a Lorentzian metric and fibers given by a Riemannian \(m\)-manifold. These spacetimes are foliated by light-like hypersurfaces.\N\NThe paper under review studies submanifolds immersed in a leaf of a generalized spacetime: in particular, an explicit formula for the mean curvature vector field is provided and several relations between the extrinsic and intrinsic geometry of the submanifolds are investigated.