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

 

Nonexistence of weakly almost complex structures on Grassmannians


Author: Zi Zhou Tang
Journal: Proc. Amer. Math. Soc. 121 (1994), 1267-1270
MSC: Primary 57R15
MathSciNet review: 1198462
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Abstract: In this paper we prove that, for $ 2 \leq k \leq n/2$, the unoriented Grassmann manifold $ {G_k}({\mathbb{R}^n})$ admits a weakly almost complex structure if and only if $ n = 2k = 4 \;$   or$ \; 6 $; for $ 3 \leq k \leq \frac{n}{2}$, none of the oriented Grassmann manifolds $ {\tilde G_k}({\mathbb{R}^n})$--except $ {\tilde G_3}({\mathbb{R}^6})$ and a few as yet undecided ones--admits a weakly almost complex structure.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1198462-5
PII: S 0002-9939(1994)1198462-5
Article copyright: © Copyright 1994 American Mathematical Society