Abstract: 
Tubular neighborhoods play an important role in modern
differential topology. The main aim of the paper is to apply these
constructions to geometry of structures on Riemannian manifolds.
Deformations of tensor structures on a normal tubular neighborhood
of a submanifold in a Riemannian manifold are considered in
section 1. In section 2, this approach is used to obtain a
K{\"a}hlerian structure on the corresponding normal tubular
neighborhood of the null section in the tangent bundle $TM$ of a
smooth manifold $M$. In section 3, we consider a new deformation
of a tensor structure on some neighborhood of a curve and
introduce the so-called {\it geometric antigravitation.}

Some results of the paper were announced in [4], [5]. The
work [3] is close to our discussion.

1. Chair of Mathematics
   Belorussian State Pedagogical University
   Sovietskaya 18
   Minsk 220050, Belarus