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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

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
MathSciNet review: 1025282
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1025282-0
PII: S 0002-9939(1990)1025282-0
Keywords: Almost complex structure, nondegenerate function, tight function, Hessian
Article copyright: © Copyright 1990 American Mathematical Society