Abstract
Some properties of Jacobi fields on a manifold of nonpositive curvature are considered. As a result, we obtain relations for derivatives of one class of functions on the manifold.
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References
M. M. Postnikov, The Variational Theory of Geodesics [in Russian], Nauka, Moscow (1965).
D. Gromoll, W. Klingenberg, and W. Meyer, Riemannsche Geometrie in Großen, Springer, Berlin (1968).
G. Misiolek, “Stability of flows of ideal fluids and the geometry of the group of diffeomorphisms,” Indiana Univ. Math. J., 42, No. 1, 215–235 (1993).
J. C. Larsen, “Geodesics and Jacobi fields in singular semi-Riemannian geometry,” Proc. Roy. Soc., London A, 446, No. 1928, 441–452 (1994).
T. Tasnadi, “The behavior of nearby trajectories in magnetic billiards,” J. Math. Phys., 37, No. 11, 5577–5598 (1996).
V. Bondarenko, “Diffusion sur variete de courbure non-positive,” C. R. Acad. Sci. Ser. 1, 324, No. 10, 1099–1103 (1997).
V. G. Bondarenko, “Covariant derivatives of Jacobi fields on a manifold of nonpositive curvature,” Ukr. Mat. Zh., 50, No. 6, 755–764 (1998).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 12, pp. 1602–1613, December, 2006.
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Bondarenko, V.G. Jacobi fields on a Riemann manifold. Ukr Math J 58, 1818–1833 (2006). https://doi.org/10.1007/s11253-006-0170-x
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DOI: https://doi.org/10.1007/s11253-006-0170-x