Suppose that (M, G) is a Riemannian manifold and f : M → R is a submersion. Then the complete lift of f, f : TM → R defined by f = ∂f ∂xi y is also a submersion. This interesting case leads us to the investigation of the level hypersurfaces of f as a submanifold of tangent bundle TM . In addition, we prolonge the level hypersurfaces of f to N̄ = (f)(0). Also, under the condition ∇̂f is a constant...

Given, in an arbitrary spacetime (M, g), a 2-dimensional timelike submanifold Σ and an observer field n on Σ, we assign gravitational, centrifugal, Coriolis and Euler forces to every particle worldline λ in Σ with respect to n. We prove that centrifugal and Coriolis forces vanish, for all λ in Σ with respect to any n, if and only if Σ is a photon 2-surface, i.e., generated by two families of li...

We study lightlike hypersurfaces of para-Sasakian manifolds tangent to the characteristic vector field. In particular, we define invariant lightlike hypersurfaces and screen semi-invariant lightlike hypersurfaces, respectively, and give examples. Integrability conditions for the distributions on a screen semi-invariant lightlike hypersurface of para-Sasakian manifolds are investigated. We obtai...

By establishing some differential geometry theory on the 1-lightlike surfaces, we show several geometric properties of the 1-lightlike surfaces which are completely different from non-lightlike surfaces. Based on these theories, we consider the singularities of the 1-lightlike surfaces in semiEuclidean 4-space with index two as an application of the theory of Legendrian singularities. We charac...

In this paper, we study radical transversal lightlike submanifolds and screen slant radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds giving some non-trivial examples of these submanifolds. Integrability conditions of distributions D and RadTM on radical transversal lightlike submanifolds and screen slant radical transversal lightlike submanifolds of indefinite pa...

We study lightlike hypersurfaces of a semi-Riemannian product manifold. We introduce a class of lightlike hypersurfaces called screen semi-invariant lightlike hypersurfaces and radical antiinvariant lightlike hypersurfaces. We consider lightlike hypersurfaces with respect to a quartersymmetric nonmetric connection which is determined by the product structure. We give some equivalent conditions ...

In this paper, we study curves in the lightlike cone. We first obtain the conformally invariant arc length in the (n+1)-dimensional lightlike cone and then characterize some curves in the 2-dimensional lightlike cone and 3-dimensional lightlike cone. MSC 2000: 53A04, 53A30, 53B30

Using screen distributions and lightlike transversal vector bundles we develop a theory of degenerate foliations of semiRiemannian manifolds. We build lightlike foliations of a semiRiemannian manifold by suspension of a group homomorphism φ : π1(B, x0) → Isom(T ). We compute the basic cohomology groups of the flow determined by a lightlike Killing vector field on a complete semi-Riemannian mani...

We first prove some results on invariant lightlike submanifolds of indefinite Sasakian manifolds. Then, we introduce a general notion of contact Cauchy-Riemann (CR) lightlike submanifolds and study the geometry of leaves of their distributions. We also study a class, namely, contact screen Cauchy-Riemann (SCR) lightlike submanifolds which include invariant and screen real subcases. Finally, we ...

We study lightlike hypersurfaces of a semi-Riemannian space form M̃(c) admitting a semi-symmetric non-metric connection. First, we construct a type of lightlike hypersurfaces according to the form of the structure vector field of M̃(c), which is called a ascreen lightlike hypersurface. Next, we prove a characterization theorem for such an ascreen lightlike hypersurface endow with a totally geodes...