标题： 复数和四元数2-Grassmannians的全测地子流形 显示英文标题

标题： Totally geodesic submanifolds of the complex and the quaternionic 2-Grassmannians

摘要： 在本文中，我分类了复2-Grassmannian和四元数2-Grassmannian中的全测地子流形。结果表明，对于这两个空间，Chen和Nagano（B.-Y. Chen, T. Nagano，“对称空间中的全测地子流形，II”，Duke Math. J. 45 (1978), 405--425）发表的秩为2的黎曼对称空间中极大全测地子流形的早期分类是不完整的。例如，当n >= 7时，G_2(H^n)包含与HP^2等距的全测地子流形，其度量被缩放使得最小截面曲率为1/5；它们在G_2(H^7)中是极大的。同样，当n >= 6时，G_2(C^n)包含与上述HP^2中包含的CP^2等距的全测地子流形；它们在G_2(C^6)中是极大的。这些子流形在引用的Chen和Nagano的论文中并未提及。 显示英文摘要

摘要： In this article, I classify the totally geodesic submanifolds in the complex 2-Grassmannians and in the quaternionic 2-Grassmannians. 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 (B.-Y. Chen, T. Nagano, "Totally geodesic submanifolds of symmetric spaces, II", Duke Math. J. 45 (1978), 405--425) is incomplete. For example, G_2(H^n) with n >= 7 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 G_2(H^7). Also G_2(C^n) with n >= 6 contains totally geodesic submanifolds which are isometric to a CP^2 contained in the HP^2 mentioned above; they are maximal in G_2(C^6). Neither submanifolds are mentioned in the cited paper by Chen and Nagano.