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On the Geometry of Almost Golden Riemannian Manifolds

Mediterranean Journal of Mathematics volume 14, Article number: 187 (2017) Cite this article

Abstract

An almost Golden Riemannian structure \((\varphi ,g)\) on a manifold is given by a tensor field \(\varphi \) of type (1,1) satisfying the Golden section relation \(\varphi ^{2}=\varphi +1\), and a pure Riemannian metric g, i.e., a metric satisfying \(g(\varphi X,Y)=g(X,\varphi Y)\). We study connections adapted to such a structure, finding two of them, the first canonical and the well adapted, which measure the integrability of \(\varphi \) and the integrability of the G-structure corresponding to \((\varphi ,g)\).

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Authors and Affiliations

  1. Departamento de Matemáticas, Estadística y Computación, Facultad de Ciencias, Universidad de Cantabria, Avda. de los Castros, s/n, 39071, Santander, Spain

    Fernando Etayo

  2. Departamento de Matemáticas, Escuela de Ingenierías Industrial e Informática, Universidad de León, Campus de Vegazana, 24071, León, Spain

    Rafael Santamaría

  3. Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad, 211019, India

    Abhitosh Upadhyay

Authors
  1. Fernando Etayo
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  2. Rafael Santamaría
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  3. Abhitosh Upadhyay
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Corresponding author

Correspondence to Rafael Santamaría.

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Etayo, F., Santamaría, R. & Upadhyay, A. On the Geometry of Almost Golden Riemannian Manifolds. Mediterr. J. Math. 14, 187 (2017). https://doi.org/10.1007/s00009-017-0991-x

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  • DOI: https://doi.org/10.1007/s00009-017-0991-x

Mathematics Subject Classification

  • Primary 53C15
  • Secondary 53C07
  • 53C10

Keywords

  • Almost Golden structure
  • pure Riemannian metric
  • adapted connection
  • first canonical connection
  • well-adapted connection