Geodesic
Analytic continuation of tensor fields along geodesics by covariant Taylor series
Teoretičeskaâ i matematičeskaâ fizika, Tome 102 (1995) no. 3, pp. 337-344

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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. 
@article{TMF_1995_102_3_a1,
     author = {A. N. Tsirulev},
     title = {Analytic continuation of tensor fields along geodesics by covariant {Taylor} series},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {337--344},
     publisher = {mathdoc},
     volume = {102},
     number = {3},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1995_102_3_a1/}
}
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A. N. Tsirulev. Analytic continuation of tensor fields along geodesics by covariant Taylor series. Teoretičeskaâ i matematičeskaâ fizika, Tome 102 (1995) no. 3, pp. 337-344. http://geodesic.mathdoc.fr/item/TMF_1995_102_3_a1/