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Geometric structures in bundles of associative algebras. (English) Zbl 1367.53011

Summary: 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.

MSC:

53A35 Non-Euclidean differential geometry
15A66 Clifford algebras, spinors
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References:

[1] Vishnevsky, V. V., Shirokov, A. P., Shurigin, V. V.: Spaces over Algebras. Kazan University, Kazan, 1965.
[2] Dubrovin, B. A., Novikov, S. P., Fomenko, A. T.: Modern Geometry. Nauka, Moscow, 1978.
[3] Penrose, R., Rindler, W.: Spinors and Space-time. Mir, Moscow, 1987. | · Zbl 0663.53013
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