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Teoreticheskaya i Matematicheskaya Fizika, 1995, Volume 102, Number 3, Pages 337–344 (Mi tmf1270)  

This article is cited in 5 scientific papers (total in 5 papers)

Analytic continuation of tensor fields along geodesics by covariant Taylor series

A. N. Tsirulev

Tver State University
Full-text PDF (861 kB) Citations (5)
References:
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.
Received: 23.03.1994
English version:
Theoretical and Mathematical Physics, 1995, Volume 102, Issue 3, Pages 245–250
DOI: https://doi.org/10.1007/BF01017874
Bibliographic databases:
Language: Russian
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
Citation in format AMSBIB
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\by A.~N.~Tsirulev
\paper Analytic continuation of tensor fields along geodesics by covariant Taylor series
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\issue 3
\pages 337--344
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\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:
    1. Manouchehr Amiri, “Joint Probability Densities on Riemannian Manifolds are Symmetric Tensor Densities”, International Journal of Computational and Applied Mathematics & Computer Science, 4 (2024), 45  crossref
    2. I. M. Potashov, “Obobschennyi algoritm vychisleniya koeffitsientov kovariantnykh ryadov Teilora”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2023, no. 2, 51–66  mathnet  crossref  elib
    3. Alexander Tsirulev, Gh. Adam, J. Buša, M. Hnatič, “A Geometric View on Quantum Tensor Networks”, EPJ Web Conf., 226 (2020), 02022  crossref
    4. 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  crossref
    5. Mattias N. R. Wohlfarth, Christian Pfeifer, “Local spacetime effects on gyroscope systems”, Phys. Rev. D, 87:2 (2013)  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:413
    Full-text PDF :146
    References:75
    First page:1
     
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