For a given -dimensional manifold we study the problem of finding the smallest integer such that admits a smooth embedding in the Euclidean space without intersecting tangent spaces. We use the Poincaré--Hopf index theorem to prove that , and construct explicit examples to show that , where denotes the -sphere. Finally, for any closed manifold , we show that .
Cite this article
Mohammad Ghomi, Tangent bundle embeddings of manifolds in Euclidean space. Comment. Math. Helv. 81 (2006), no. 1, pp. 259–270DOI 10.4171/CMH/51