Geometric structures; bundles of linear algebra; vector bundles on smooth manifolds
The article deals with bundles of linear algebra as a specifications of the case of smooth manifold. It allows to introduce on smooth manifold a metric by a natural way. The transfer of geometric structure arising in the linear spaces of associative algebras to a smooth manifold is also presented.
 Vishnevsky, V. V., Shirokov, A. P., Shurigin, V. V.: Spaces over Algebras. Kazan University, Kazan, 1965.
 Dubrovin, B. A., Novikov, S. P., Fomenko, A. T.: Modern Geometry. Nauka, Moscow, 1978.