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Mat. Zametki, 1974, Volume 15, Issue 4, Pages 603–612 (Mi mz7384)  

Transformations in hypercomplex Riemannian spaces

V. V. Navrozov

Kirov Polytechnic Institute

Abstract: It is well known that an integrable regular $H$-structure induces on a real manifold $M_n$ the structure of a hypercomplex analytic manifold ($h$-manifold) $\mathop M\limits^* _m$. We prove that the Lie derivative of a pure tensor $T$ on $M_n$ is an $h$-derivative of Lie providing $T$ is $h$-analytic. With the $h$-derivative of Lie there is associated on $\mathop M\limits^* _m$ the hypercomplex derivative of Lie. This enables us to associate to the motions and affine collineations in the Riemannian space $\mathop V\limits^* _m$ corresponding transformations in a real space $V_n$.

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English version:
Mathematical Notes, 1974, 15:4, 356–361

Bibliographic databases:

UDC: 513
Received: 15.06.1973

Citation: V. V. Navrozov, “Transformations in hypercomplex Riemannian spaces”, Mat. Zametki, 15:4 (1974), 603–612; Math. Notes, 15:4 (1974), 356–361

Citation in format AMSBIB
\Bibitem{Nav74}
\by V.~V.~Navrozov
\paper Transformations in hypercomplex Riemannian spaces
\jour Mat. Zametki
\yr 1974
\vol 15
\issue 4
\pages 603--612
\mathnet{http://mi.mathnet.ru/mz7384}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=350652}
\zmath{https://zbmath.org/?q=an:0316.53031}
\transl
\jour Math. Notes
\yr 1974
\vol 15
\issue 4
\pages 356--361
\crossref{https://doi.org/10.1007/BF01095128}


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