On totally geodesic spheres in Grassmannians and 𝑂(𝑛)

Wang, Qi Ming

doi:10.1090/S0002-9939-1990-0994793-6

On totally geodesic spheres in Grassmannians and $\textrm {O}(n)$
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Proc. Amer. Math. Soc. 108 (1990), 811-815 Request permission

Abstract:

It was shown in [5] that the generators of the homotopy groups of the stable orthogonal groups and the stable Grassmannians can be represented by embedded totally geodesic spheres of constant curvature. In this paper we prove that all elements of the above-mentioned homotopy groups can be represented by such spheres.

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