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On a class of submanifolds in a tangent bundle with a $g$-natural metric

Volume 150 / 2017

Stanisław Ewert-Krzemieniewski Colloquium Mathematicum 150 (2017), 121-133 MSC: Primary 53B20, 53C07, Secondary 53B21, 53B25. DOI: 10.4064/cm7128s-2-2017 Published online: 1 September 2017

Abstract

An isometric immersion of a Riemannian manifold $M$ into a Riemannian manifold $N$ gives rise in a natural way to the immersion of the tangent bundle $TM$ into the tangent bundle $TN$ with a non-degenerate $g$-natural metric $G.$ It turns out that the normal bundle of the image of $TM$ is completely determined by the normal bundle of $M.$ The cases of $M$ being either totally geodesic or pseudo-umbilical are discussed.

Authors

  • Stanisław Ewert-KrzemieniewskiSchool of Mathematics
    West Pomeranian University of Technology
    Al. Piastów 17
    70-310 Szczecin, Poland
    e-mail

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