  In this series of papers 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 part of the series five-dimensional tangent vectors are
introduced as abstract objects related in a certain way to ordinary
four-dimensional tangent vectors. I then make a formal study of their basic
algebraic properties and of their differential properties in flat space-time.
In conclusion I consider some examples of quantities described by five-vectors
and five-tensors.
