Prolongations of tensor fields and connections to tangent bundles I General theory

Kentaro YANO; Shoshichi KOBAYASHI

doi:10.2969/jmsj/01820194

Prolongations of tensor fields and connections to tangent bundles I

General theory

Kentaro YANO, Shoshichi KOBAYASHI

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JOURNAL FREE ACCESS

1966 Volume 18 Issue 2 Pages 194-210

DOI https://doi.org/10.2969/jmsj/01820194

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Published: 1966 Received: December 13, 1965 Available on J-STAGE: September 26, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 26, 2006 Reason for correction: - Correction: CITATION Details: Right : [1] M. Berger, Les espaces sy métriques non compacts, Ann. Sci. Ecole Norm., Sup., (3) 74 (1957), 85-177.
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[5] A. J. Ledger and K. Yano, The tangent bundle of a locally symmetric space, J. London Math. Soc., 40 (1965), 487-492.
[6] T. Nagano, Transformation groups on symmetric spaces, to appear in Trans. Amer. Math. Soc..
[7] S. Sasaki, On the differential geometry of tangent bundles of Riemannian manifolds, Tôhoku Math. J., 10 (1958), 338-354.
[8] S. Tanno, An almost complex structure of the tangent bundle of an almost contact manifold, Tôhoku Math. J., 17 (1965), 7-15.
[9] P. Tondeur, Structure presque kählérienne naturelle sur la fibré des vecteurs covariants d'une variété riemannienne, C. R. Acad. Sci. Paris, 254 (1962), 407-408.
[10] A. Weil, Théorie des points proches sur les variétés différentiables, Colloque de géométrie différentielle, Strasbourg, (1953), 111-117.
[11] K. Yano, The theory of Lie derivatives and its applications, North Holland Pub. Co., Amsterdam, 1957.
[12] K. Yano, On a structure f satisfying f³+f=0, Technical Report, University of Washington, 1961.
[13] K. Yano, On a structure defined by a tensor field f of type (1, 1) satisfying f³+f=0, Tensor, 14 (1963), 99-109.
[14] K. Yano and E. T. Davies, On the tangent bundle of Finsler and Riemannian manifolds, Rend. Circ. Mat. Palermo, 12 (1963), 211-228.
[15] K. Yano and A. J. Ledger, Linear connections on tangent bundles, J. London Math. Soc., 39 (1964), 495-500.

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