ON LEVEL HYPERSURFACES OF THE COMPLETE LIFT OF A SUBMERSION

Abstract

Suppose that (M, G) is a Riemannian manifold and f : M -> R is a submersion. Then the complete lift of f, f(c) : TM -> R defined by f(c) = partial derivative f/partial derivative x(i) y(i) is also a submersion. This interesting case leads us to the investigation of the level hypersurfaces of f(c) as a submanifold of tangent bundle TM. In addition, we prolonge the level hypersurfaces of f to (N) over bar = (f(c))(-1)(0). Also, under the condition (del) over capf is a constant, we show that (N) over bar has a light like structure with induced metric (G) over bar from G(c).