Abstract:
Newtonian dynamical systems that accept the normal shift on an arbitrary Riemannian manifold are considered. For them the determinating equations making the weak normality condition are derived. The expansion for the algebra of tensor fields is constructed.
Citation:
A. Yu. Boldin, V. V. Dmitrieva, S. S. Safin, R. A. Sharipov, “Dynamical systems on a Riemannian manifold that admit normal shift”, TMF, 103:2 (1995), 256–266; Theoret. and Math. Phys., 103:2 (1995), 543–549
\Bibitem{BolDmiSaf95}
\by A.~Yu.~Boldin, V.~V.~Dmitrieva, S.~S.~Safin, R.~A.~Sharipov
\paper Dynamical systems on a~Riemannian manifold that admit normal shift
\jour TMF
\yr 1995
\vol 103
\issue 2
\pages 256--266
\mathnet{http://mi.mathnet.ru/tmf1300}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1470946}
\zmath{https://zbmath.org/?q=an:0854.58031}
\transl
\jour Theoret. and Math. Phys.
\yr 1995
\vol 103
\issue 2
\pages 543--549
\crossref{https://doi.org/10.1007/BF02274031}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995TD56100006}
Linking options:
https://www.mathnet.ru/eng/tmf1300
https://www.mathnet.ru/eng/tmf/v103/i2/p256
This publication is cited in the following 4 articles:
R. A. Sharipov, “Dynamic Systems Admitting the Normal Shift and Wave Equations”, Theoret. and Math. Phys., 131:2 (2002), 651–665
E. V. Ferapontov, R. A. Sharipov, “On first-order conservation laws for systems of hydronamic type equations”, Theoret. and Math. Phys., 108:1 (1996), 937–952
A. Yu. Boldin, A. A. Bronnikov, V. V. Dmitrieva, R. A. Sharipov, “Complete normality conditions for the dynamical systems on Riemannian manifolds”, Theoret. and Math. Phys., 103:2 (1995), 550–555
R. A. Sharipov, “Metrizability of dynamical systems by a conformally equivalent metric”, Theoret. and Math. Phys., 103:2 (1995), 556–560