Invariant null rigged hypersurfaces of indefinite nearly \(\alpha\)-Sasakian manifolds (Q6548297)

The theory of null submanifolds of a semi-Riemannian manifold is one of the important topics of differential geometry. Null hypersurfaces appear in general relativity as models of different types of black hole horizons. In this case the induced metric on the submanifold is degenerate, and thus the study becomes more difficult and is strikingly different from the study of nondegenerate submanifolds. Recently, \textit{M. Gutiérrez} and \textit{B. Olea} [Math. Nachr. 289, No. 10, 1219--1236 (2016; Zbl 1345.53021)] developed new techniques to endow a null hypersurface in a Lorentzian manifold with a Riemannian metric. This is based on an arbitrary choice of a transverse vector field, called the rigging field, from which the one constructs a null section, called the rigged field and a screen distribution. This technique improves the dependency of the geometric objects on only the choice of a unique object, namely the rigging field.\N\NIn this paper, the authors investigate the effect of rigging on the null hypersurfaces of almost contact structures especially for indefinite nearly \(\alpha\)-Sasakian structures.