TY  - JOUR
T1  - Normalized Null hypersurfaces of Indefinite Kähler Manifolds
AU  - Kumar, Rakesh
AU  - Sıngh, Amrınder Pal
AU  - Atındogbe, Cyriaque
AU  - Jain, Varun
PY  - 2023
DA  - April
Y2  - 2022
DO  - 10.36890/iejg.1148612
JF  - International Electronic Journal of Geometry
JO  - Int. Electron. J. Geom.
PB  - Kazım İlarslan
WT  - DergiPark
SN  - 1307-5624
SP  - 417
EP  - 434
VL  - 16
IS  - 1
LA  - en
AB  - 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.
KW  - Indefinite Kähler manifolds
KW  - Null hypersurfaces
KW  - Rigging vector field
KW  - Induced Ricci tensor
KW  - Null sectional curvature
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UR  - https://doi.org/10.36890/iejg.1148612
L1  - https://dergipark.org.tr/en/download/article-file/2556882
ER  -