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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
DOI: https://doi.org/10.1090/S0002-9939-1994-1198462-5
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 $n = 2k = 4 \; \text {or} \; 6$; 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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Article copyright: © Copyright 1994 American Mathematical Society