Abstract:
It is shown that in a certain normal neighborhood of a submanifold – the analog of a normal neighborhood of a point – the covariant derivatives of all orders of an arbitrary tensor field and of the curvature and torsion along geodesics normal to the submanifold, taken at points of the submanifold, determine under conditions of analyticity the given tensor field by Taylor series with tensor coefficients. Explicit expressions are obtained that provide a recursive procedure for calculating the coefficients of the series in any order. Special cases of the expansion of the components of a pseudo-Riemannian metric with respect to a metric connection without torsion for a point and hypersurface are considered.
Citation:
A. N. Tsirulev, “Analytic continuation of tensor fields along geodesics by covariant Taylor series”, TMF, 102:3 (1995), 337–344; Theoret. and Math. Phys., 102:3 (1995), 245–250
\Bibitem{Tsi95}
\by A.~N.~Tsirulev
\paper Analytic continuation of tensor fields along geodesics by covariant Taylor series
\jour TMF
\yr 1995
\vol 102
\issue 3
\pages 337--344
\mathnet{http://mi.mathnet.ru/tmf1270}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1348845}
\zmath{https://zbmath.org/?q=an:0857.53009}
\transl
\jour Theoret. and Math. Phys.
\yr 1995
\vol 102
\issue 3
\pages 245--250
\crossref{https://doi.org/10.1007/BF01017874}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995RZ02000002}
Linking options:
https://www.mathnet.ru/eng/tmf1270
https://www.mathnet.ru/eng/tmf/v102/i3/p337
This publication is cited in the following 5 articles:
Manouchehr Amiri, “Joint Probability Densities on Riemannian Manifolds are Symmetric Tensor Densities”, International Journal of Computational and Applied Mathematics & Computer Science, 4 (2024), 45
I. M. Potashov, “Obobschennyi algoritm vychisleniya koeffitsientov kovariantnykh ryadov Teilora”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2023, no. 2, 51–66
Alexander Tsirulev, Gh. Adam, J. Buša, M. Hnatič, “A Geometric View on Quantum Tensor Networks”, EPJ Web Conf., 226 (2020), 02022
Ivan Potashov, Alexander Tsirulev, Gh. Adam, J. Buša, M. Hnatič, D. Podgainy, “Computational Algorithm for Covariant Series Expansions in General Relativity”, EPJ Web Conf., 173 (2018), 03021
Mattias N. R. Wohlfarth, Christian Pfeifer, “Local spacetime effects on gyroscope systems”, Phys. Rev. D, 87:2 (2013)