On a class of submanifolds in tangent bundle with g- natural metric
  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. 
Stanis{\l}aw Ewert-Krzemieniewski
math.DG