Abstract
Jacobian determines a bundle with total space consisting of orientation-preserving diffeomorphisms of a (connected) manifold over the space of positive functions on this manifold (with integral equal to volume for a compact manifold). It is proved that, for the \(n\)-sphere with standard metric, there is a unique connection on this bundle that is invariant with respect to all isometries of the sphere, and a description of this connection is given.
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Translated from Funktsional'nyi Analiz i ego Prilozheniya, 2021, Vol. 55, pp. 82–84 https://doi.org/10.4213/faa3914.
Translated by S. M. Gusein-Zade
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Gusein-Zade, S.M. Connection on the Group of Diffeomorphisms as a Bundle Over the Space of Functions. Funct Anal Its Appl 55, 242–244 (2021). https://doi.org/10.1134/S0016266321030072
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DOI: https://doi.org/10.1134/S0016266321030072