Abstract
Let $G(k,n)$ be the complex Grassmann manifold of $k$-planes in $\mathbb C^{k+n}$. In this note, we show that for $1< k<n$ and for any selfmap $f:G(k,n)\to G(k,n)$, there exists a $k$-plane $V^k\in G(k,n)$ such that $f(V^k)\cap V^k\ne \{0\}$.
Citation
Thaís F. M. Monis. Northon C. L. Penteado. Sérgio T. Ura. Peter Wong. "A note on nontrivial intersection for selfmaps of complex Grassmann manifolds." Bull. Belg. Math. Soc. Simon Stevin 24 (4) 665 - 672, december 2017. https://doi.org/10.36045/bbms/1515035015
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