Metrics and Connections on the Bundle of Affinor Frames

Citation:

Habil FATTAYEV,Arif SALIMOV.Metrics and Connections on the Bundle of Affinor Frames[J].Chinese Annals of Mathematics B,2021,42(1):121~134
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Authors:

Habil FATTAYEV; Arif SALIMOV
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.

Keywords:

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

Classification:

53C05; 53B20.
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