The tightness of certain almost complex submanifolds

Abstract:

This paper contains a proof of the following fact. If a map $f$ from a connected Riemannian manifold with an almost complex structure into a euclidean space has the following properties: (a) $f$ is nondegenerate and (b) for almost all height functions, the linear Hessian of the composition with $f$ commutes with the almost complex structure, then $f$ is tight. This gives some information about the homology groups of the manifold. This result yields a new proof of a well-known theorem of R. Bott.