On a class of submanifolds in tangent bundle with g - natural metric -   normal lift
  An isometric immersion of a Riemannian manifold $M$ into a Riemannian manifold $N$ gives rise in a natural way to variety of immersions into the tangent bundle $TN$ with a non-degenerate $g-$ natural metric $G$. In the paper we introduce and study an immersion into $TN$ defined by the immersion $f:M\longrightarrow N$ itself and the normal bundle. 
Stanis{\l}aw Ewert-Krzemieniewski
math.DG