Totally Geodesic Submanifolds of the Complex and the Quaternionic 2-grassmannians
نویسنده
چکیده
In this article, the totally geodesic submanifolds in the complex 2Grassmannian G2(C) and in the quaternionic 2-Grassmannian G2(H) are classified. It turns out that for both of these spaces, the earlier classification of maximal totally geodesic submanifolds in Riemannian symmetric spaces of rank 2 published by Chen and Nagano (1978) is incomplete. For example, G2(H) with n ≥ 5 contains totally geodesic submanifolds isometric to a HP 2, its metric scaled such that the minimal sectional curvature is 1 5 ; they are maximal in G2(H). G2(C) with n ≥ 4 contains totally geodesic submanifolds which are isometric to a CP 2 contained in the HP 2 mentioned above; they are maximal in G2(C). Neither submanifolds are mentioned by Chen and Nagano.
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