Summary
The tangent bundle is regarded as an almost product manifold. Connections adapted to this structure are introduced. Use is made of the theory of submersions,
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References
P. Dombroski,On the geometry of the tangent bundle, J. Reine und Angew. Math., 210 (1962), 73–88.
A. Gray,Pseudo-Riemannian almost product manifolds and submersions. J. Math. and Mech., 16 (1967), 715–737.
B. O’Neill,The fundamental equations of a submersion, Michigan J. of Math., 13 (1966), 459–469.
S. Kobayashi andK. Nomizu,Foundations of differential geometry, Vol. 1, Interscience, New York 1963.
S. Sasaki,On the differential geometry of tangent bundles of Riemannian manifolds, Tohoku Math. J., 10 (1958), 338–354.
K. Yano andS. Ishihara,Horizontal lifts of tensor fields and connections to tangent bundles, J. Math. and Mech. 16 (1967), 1015–1030.
K. Yano andA. J. Ledger,Linear connections on tangent bundles, J. London Math. Soc, 39 (1964), 495–500.
A. G Walker,Connections for parallel distributions in the large, Quarterly J. of Math. (2), 9 (1958) 221–231.
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Entrata in Redazione il 23 agosto 1968.
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Davies, E.T. On the curature of the tangent bundle. Annali di Matematica 81, 193–204 (1969). https://doi.org/10.1007/BF02413503
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DOI: https://doi.org/10.1007/BF02413503