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Curvature colligations

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Abstract

It is shown that the curvature operators of a connection colligation may be included in a natural way in an operator colligation. This operator colligation is called the curvature colligation. As an application it is shown that if several operators are included in an operator colligation, then all their commutators may be included in a natural way in a new operator colligation. In particular a notion of the commutator of two operator colligations is obtained.

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References

  1. Gauchman, H.: Operator colligations on differentiable manifolds. Toeplitz Centennial, Operator Theory and Applications, vol. 4, Birkhäuser (1982), 271–302.

    Google Scholar 

  2. Gauchman, H.: Connection colligations on Hilbert bundles, Integral Equations and Operator Theory, vol. 6/1 (1983), 31–58.

    Google Scholar 

  3. Gauchman, H.: Connection colligations of the second order, Integral Equations and Operator Theory, vol. 6/2 (1983), 184–205.

    Google Scholar 

  4. Kobayashi, S. and Nomizu, K.: Foundations of Differential Geometry, vol. 1, J. Wiley, 1963.

  5. Livšic, M. S. and Jancevich, A.A.: Theory of Operator Colligations in Hilbert Space, J. Wiley, 1979.

  6. Livšic, M.S. and Vaxman, L.L.: Open geometry and operator colligations, Ukrain. Geom. Sbornik, 15 (1974), 16–35 (in Russian).

    Google Scholar 

  7. Raševskiî, P.K.: Riemannian Geometry and Tensor Analysis, Nauka, Moscow, 1967 (in Russian).

    Google Scholar 

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Gauchman, H. Curvature colligations. Integr equ oper theory 7, 45–59 (1984). https://doi.org/10.1007/BF01204913

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  • DOI: https://doi.org/10.1007/BF01204913

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