On a class of submanifolds in a tangent bundle with a $g$-natural metric
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.
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
Affiliations des auteurs :
Stanisław Ewert-Krzemieniewski 1
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author = {Stanis{\l}aw Ewert-Krzemieniewski},
title = {On a class of submanifolds in a tangent bundle with a $g$-natural metric},
journal = {Colloquium Mathematicum},
pages = {121--133},
publisher = {mathdoc},
volume = {150},
number = {1},
year = {2017},
doi = {10.4064/cm7128s-2-2017},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm7128s-2-2017/}
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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
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