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Invariant points of maps between Grassmannians

Author(s): Kalyan Mukherjea; Parameswaran Sankaran
Journal: Proc. Amer. Math. Soc. 124 (1996), 649-653.
MSC (1991): Primary 55M20, 54H25
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Abstract: We show that for a very large class of integers $l<k<n$ and any map $f\colon G_k(\mathbb R^n)\to G_l(\mathbb R^n)$ between Grassmannians, there is some $k$ -plane of $\mathbb R^n$ which is mapped into a subspace of itself.

References:

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P: R. R. Patterson, The square preserving algebra endomorphisms of Quart. J. Math. Oxford Ser. (2) 29 (1978), 225--240. MR 80g:55033
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Z: P. Zvengrowski, A -fold vector product in $\mathbb R^8$ , Comment. Math. Helv. 40 (1966), 149--152. MR 32:8343


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