Normalized Null hypersurfaces of Indefinite Kähler Manifolds

Authors : Amrınder Pal SINGH, Cyriaque ATINDOGBE, Rakesh KUMAR, Varun JAİN

Pages : 417-434

Doi:10.36890/iejg.1148612

View : 9 | Download : 5

Publication Date : 2023-04-30

Article Type : Research Paper

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