Metrics and Connections on the Bundle of Affinor Frames

Abstract

In this paper the authors consider the bundle of affinor frames over a smooth manifold, define the Sasaki metric on this bundle, and investigate the Levi-Civita connection of Sasaki metric. Also the authors determine the horizontal lifts of symmetric linear connection from a manifold to the bundle of affinor frames and study the geodesic curves corresponding to the horizontal lift of the linear connection.

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Correspondence to Arif Salimov.

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Fattayev, H., Salimov, A. Metrics and Connections on the Bundle of Affinor Frames. Chin. Ann. Math. Ser. B 42, 121–134 (2021). https://doi.org/10.1007/s11401-021-0248-7

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Keywords

  • Bundle of affinor frames
  • Riemannian manifold
  • Sasaki metric
  • Horizontal lift
  • Geodesic curve

2000 MR Subject Classification

  • 53C05
  • 53B20