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Lifts of Foliated Linear Connectionsto the Second Order Transverse Bundles

Vadim V. Shurygin, Svetlana K. Zubkova (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The second order transverse bundle T 2 M of a foliated manifold M carries a natural structure of a smooth manifold over the algebra 𝔻 2 of truncated polynomials of degree two in one variable. Prolongations of foliated mappings to second order transverse bundles are a partial case of more general 𝔻 2 -smooth foliated mappings between second order transverse bundles. We establish necessary and sufficient conditions under which a 𝔻 2 -smooth foliated diffeomorphism between two second order transverse bundles maps...

Lightlike hypersurfaces of an indefinite Kaehler manifold of a quasi-constant curvature

Dae Ho Jin, Jae Won Lee (2019)

Communications in Mathematics

We study lightlike hypersurfaces M of an indefinite Kaehler manifold M ¯ of quasi-constant curvature subject to the condition that the characteristic vector field ζ of M ¯ is tangent to M . First, we provide a new result for such a lightlike hypersurface. Next, we investigate such a lightlike hypersurface M of M ¯ such that (1) the screen distribution S ( T M ) is totally umbilical or (2) M is screen conformal.

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