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Lifts of tensor fields to the frame bundle

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Abstract

LetM be a differentiable manifold,T M its tangent bundle andF M its frame bundle. The theory of lifts toT M of tensor fields onM has been extensively studied by many authors. In this paper, a similar theory for the frame bundle is developed by introducing the complete, horizontal and diagonal lifts toF M of tensor fields onM, with the aim of making this study as closely comparable with that forT M as possible.

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References

  1. Cordero L. A., De Leon M.,On the differential geometry of the frame bundle, to appear.

  2. Kobayashi S., Nomizu K.,Foundations of Differential Geometry, vol. I, Interscience, New York 1963.

    MATH  Google Scholar 

  3. Mok K. P.,On the differential geometry of frame bundles of Riemannian manifolds, J. Reine Angew Math.302 (1978), 16–31.

    MATH  MathSciNet  Google Scholar 

  4. Mok K. P.,Complete lif of tensor fields and connections to the frame bundle, Proc. London Math. Soc. (3)32 (1979), 72–88.

    Article  MathSciNet  Google Scholar 

  5. Okubo T.,On the differential geometry of frame bundles F(X n),n=2m, Mem. Defense Acad.5 (1965), 1–17.

    MathSciNet  Google Scholar 

  6. Okubo T.,On the differential geometry of frame bundles, Ann. Mat. pura Appl. (4)72 (1966), 29–44.

    MATH  MathSciNet  Google Scholar 

  7. Sasaki S.,On the differential geometry of tangent bundles of Riemannian manifolds, Tôhoku Math. J.10 (1958), 338–354.

    Article  MATH  Google Scholar 

  8. Terrier J. M.,Linear connections and almost complex structures, Proc. Amer. Math. Soc.49 (1975), 59–65.

    Article  MATH  MathSciNet  Google Scholar 

  9. Wong Y. C.,Recurrent tensors on a linearly connected differentiable manifold, Trans. Amer. Math. Soc.99 (1961), 325–341.

    Article  MATH  MathSciNet  Google Scholar 

  10. Yano K., Ishihara, S.,Horizontal lifts of tensor fields and connections to tangent bundles, Jour. Math. and Mech.16 (1967), 1015–1030.

    MATH  MathSciNet  Google Scholar 

  11. Yano K., Ishihara S.,Tangent and Cotagent Bundles, Differential Geometry, Marcel Dekker, New York 1973.

    Google Scholar 

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Authors and Affiliations

  1. Departmento de Geometria y Topologia Facultad de Matematicas, Universidad de Santiago de Compostela, Spain

    Luis A. Cordero & Manuel de Leon

Authors
  1. Luis A. Cordero
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  2. Manuel de Leon
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Cordero, L.A., de Leon, M. Lifts of tensor fields to the frame bundle. Rend. Circ. Mat. Palermo 32, 236–271 (1983). https://doi.org/10.1007/BF02844834

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  • DOI: https://doi.org/10.1007/BF02844834

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