On a class of submanifolds in tangent bundle with g - natural metric - normal lift

Abstract

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 $f:M⟶N$ itself and the normal bundle.

arXiv commentThe versions of my article "On a class of submanifolds in tangent bundle with g - natural metric - normal lift" published on Arxiv.org Before April, 23, 2018, contain mistakes. Firstly, starting from Example 7 the assumption codimM > 1 is essential. Secondly, the first formula on page 16 is too short - some terms are omitted. Consequently, the final theorem is not true