Geodesic
On a class of submanifolds in a tangent bundle with a $g$-natural metric
Stanisław Ewert-Krzemieniewski1
1 School of Mathematics West Pomeranian University of Technology Al. Piastów 17 70-310 Szczecin, Poland
Colloquium Mathematicum, Tome 150 (2017) no. 1, pp. 121-133.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/cm7128s-2-2017
Keywords: isometric immersion riemannian manifold riemannian manifold gives rise natural immersion tangent bundle tangent bundle non degenerate g natural metric nbsp turns out normal bundle image completely determined normal bundle nbsp cases being either totally geodesic pseudo umbilical discussed

Stanisław Ewert-Krzemieniewski 1

1 School of Mathematics West Pomeranian University of Technology Al. Piastów 17 70-310 Szczecin, Poland 
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Stanisław Ewert-Krzemieniewski. On a class of submanifolds in a tangent bundle with a $g$-natural metric. Colloquium Mathematicum, Tome 150 (2017) no. 1, pp. 121-133. doi : 10.4064/cm7128s-2-2017. http://geodesic.mathdoc.fr/articles/10.4064/cm7128s-2-2017/

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