On a class of submanifolds in a tangent bundle with a $g$-natural metric
Tom 150 / 2017
Colloquium Mathematicum 150 (2017), 121-133 MSC: Primary 53B20, 53C07, Secondary 53B21, 53B25. DOI: 10.4064/cm7128s-2-2017 Opublikowany online: 1 September 2017
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.