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Geometry and Topology of Some Fibered Riemannian Manifolds

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Abstract

We investigate a principal G-bundle with G-invariant Riemannian metric on its total space. We derive formulas describing the Levi-Civita connection and curvatures in two-dimensional directions. We obtain estimates of the influence of properties of sectional curvatures to topological invariants of the bundle.

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Authors and Affiliations

  1. Nizhny Novgorod State University, pr. Gagarina 23, Nizhny Novgorod, 603950, Russia

    E. I. Yakovlev & T. A. Gonchar

Authors
  1. E. I. Yakovlev
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  2. T. A. Gonchar
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Correspondence to E. I. Yakovlev.

Additional information

Original Russian Text © E.I. Yakovlev and T.A. Gonchar, 2018, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, No. 2, pp. 77–95.

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Yakovlev, E.I., Gonchar, T.A. Geometry and Topology of Some Fibered Riemannian Manifolds. Russ Math. 62, 69–85 (2018). https://doi.org/10.3103/S1066369X18020081

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  • DOI: https://doi.org/10.3103/S1066369X18020081

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