  This article is a summary of a series of papers to be published where I
examine a special kind of geometric objects that can be defined in space-time
--- five-dimensional tangent vectors. Similar objects exist in any other
differentiable manifold, and their dimension is one unit greater than that of
the manifold. Like ordinary tangent vectors, the considered five-dimensional
vectors and the tensors constructed out of them can be used for describing
certain local quantities and in this capacity find direct application in
physics. For example, such familiar physical quantities as the stress-energy
and angular momentum tensors prove to be parts of a single five-tensor. In this
paper I describe several different mathematical definitions of five-dimensional
tangent vectors, discuss their basic algebraic and differential properties, and
speak about their possible application in the theory of gravity and in gauge
theories.
