Normalized Null hypersurfaces of Indefinite Kähler Manifolds

Year 2023, Volume: 16 Issue: 1, 417 - 434, 30.04.2023

Amrınder Pal Sıngh , Cyriaque Atındogbe , Rakesh Kumar , Varun Jain

https://doi.org/10.36890/iejg.1148612

Abstract

We study null hypersurfaces of indefinite Kähler manifolds and by taking the advantages of the almost complex structure $J$, we select a suitable rigging $\zeta$, which we call the $J-$rigging, on the null hypersurface. This suitable rigging enables us to build an associated Hermitian metric $\breve{g}$ on the ambient space and which is restricted into a non-degenerated metric $\widetilde{g}$ on the normalized null hypersurface. We derive Gauss-Weingarten type formulae for null hypersurface $M$ of an indefinite Kähler manifold $\overline{M}$ with a fixed closed Killing $J-$rigging for $M$. Later, we establish some relations linking the curvatures, null sectional curvatures, Ricci curvatures, scalar curvatures etc. of the ambient manifold and normalized null hypersurface.

Keywords

Indefinite Kähler manifolds, Null hypersurfaces, Rigging vector field, Induced Ricci tensor, Null sectional curvature

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