The tightness of certain almost complex submanifolds

Author:
Cristián U. Sánchez

Journal:
Proc. Amer. Math. Soc. **110** (1990), 807-811

MSC:
Primary 53C40; Secondary 53C15, 53C30, 57T15

DOI:
https://doi.org/10.1090/S0002-9939-1990-1025282-0

MathSciNet review:
1025282

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper contains a proof of the following fact. If a map from a connected Riemannian manifold with an almost complex structure into a euclidean space has the following properties: (a) is nondegenerate and (b) for almost all height functions, the linear Hessian of the composition with commutes with the almost complex structure, then 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.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1990-1025282-0

Keywords:
Almost complex structure,
nondegenerate function,
tight function,
Hessian

Article copyright:
© Copyright 1990
American Mathematical Society