Horizontal lift of symmetric connections to the bundle of volume forms \(\mathcal{V}\)

Anna Gasior

Abstract


In this paper we present the horizontal lift of a symmetric affine connection with respect to another affine connection to the bundle of volume forms \(\mathcal{V}\) and give formulas for its curvature tensor, Ricci tensor and the scalar curvature. Next, we give some properties of the horizontally lifted vector fields and certain infinitesimal transformations. At the end, we consider some substructures of a \(F(3, 1)\)-structure on \(\mathcal{V}\).

Keywords


Horizontal lift; \(\pi\)-conjugate connection; Killing field; infinitesimal transformation; \(F(3, 1)\)-structure; FK, FAK, FNK, FQK, FH-structure

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References


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DOI: http://dx.doi.org/10.2478/v10062-010-0004-z
Date of publication: 2016-07-29 22:06:16
Date of submission: 2016-07-29 18:19:30


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