Abstract
In the present paper we obtain a new proof of the fundamental equations of F-planar mappings of manifolds with affine connections. We discuss alternative ways in the definition of F-planar mappings.
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References
C.-L. Bejan and S. L. Druta-Romaniuc, “F-geodesics on manifolds,” Filomat 29, 2367–2379 (2015).
D. V. Beklemishev, “Differential geometry of spaces with almost complex structure,” Itogi Nauki Tekh., Geom. 1963, 165–212 (1963).
L. P. Eisenhart, Riemannian Geometry (Princeton Univ. Press, Princeton, 1949).
L. E. Evtushik, Ü. G. Lumiste, N. M. Ostianu, and A. P. Shirokov, “Differential-geometric structures on manifolds,” Itogi Nauki Tekh., Ser. Probl. Geom. 9, 1–248 (1979).
V. E. Fomin, “Projective correspondence of two Riemannian spaces of infinite dimension,” Tr. Geom. Semin. 10, 86–96 (1978).
I. Hinterleitner and J. Mikeš, “On F-planar mappings of spaces with affine connections,” Note Mat. 27, 111–118 (2007).
I. Hinterleitner, J. Mikeš, and P. Peška, “On F 2 ε-planar mappings of (pseudo-) Riemannian manifolds,” Arch. Math. Brno 50, 287–295 (2014).
I. Hinterleitner, J. Mikeš, and J. Stránská, “Infinitesimal F-planar transformations,” Russ. Math. 52, 13–18 (2008).
J. Mikeš, “Geodesic mappings of affine-connected and Riemannian spaces,” J. Math. Sci. 78, 311–333 (1996).
J. Mikeš, “Holomorphically projective mappings and their generalizations,” J. Math. Sci. 89, 1334–1353 (1998).
J. Mikeš, A. Vanžurová, and I. Hinterleitner, Geodesic Mappings and Some Generalizations (Palacky Univ. Press, Olomouc, 2009).
J. Mikešet al., Differential Geometry of Special Mappings (Palacky Univ. Press, Olomouc, 2015).
J. Mikešand N. S. Sinyukov, “Quasiplanar mappings of spaces with affine connection,” Sov. Math. 27, 63–70 (1983).
A. Z. Petrov, “Modeling of the paths of test particles in gravitation theory,” Grav. Theory Relativ., Nos. 4–5, 7–21 (1968).
A. P. Shirokov, “Spaces over algebras and their applications,” J. Math. Sci. 108, 232–248 (2002).
P. A. Shirokov, Selected Investigations on Geometry (Kazan Gos. Univ., Kazan, 1966) [in Russian].
N. S. Sinyukov, Geodesic Mappings of Riemannian Spaces (Nauka,Moscow, 1979) [in Russian].
N. V. Talantova and A. P. Shirokov, “Projective models of unitary spaces of constant curvature over an algebra of dual numbers,” Tr. Geom. Sem. 16, 103–110 (1984).
V. V. Vishnevskii, A. P. Shirokov, and V. V. Shurygin, Spaces over Algebras (Kazan. Gos. Univ., Kazan, 1985) [in Russian].
K. Yano, Differential Geometry of Complex and almost Comlex Spaces (Pergamon, Oxford, 1965).
M. Lj. Zlatanović, L. S. Velimirović, and M. S. Stanković, “Necessary and sufficient conditions for equitorsion geodesic mapping,” J. Math. Anal. Appl. 435, 578–592 (2016).
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Submitted by F. G. Avkhadiev
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Hinterleitner, I., Mikeš, J. & Peška, P. Fundamental equations of F-planar mappings. Lobachevskii J Math 38, 653–659 (2017). https://doi.org/10.1134/S1995080217040096
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DOI: https://doi.org/10.1134/S1995080217040096