Geodesic
Geometry and topology of some fibered Riemannian manifolds
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2018), pp. 77-95

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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.
Keywords: principal bundle, $G$-connection, Riemannian manifold, Levi–Civita connection, sectional curvature. 
@article{IVM_2018_2_a7,
     author = {E. I. Yakovlev and T. A. Gonchar},
     title = {Geometry and topology of some fibered {Riemannian} manifolds},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {77--95},
     publisher = {mathdoc},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_2_a7/}
}
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E. I. Yakovlev; T. A. Gonchar. Geometry and topology of some fibered Riemannian manifolds. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2018), pp. 77-95. http://geodesic.mathdoc.fr/item/IVM_2018_2_a7/