PARALLEL SUBMANIFOLDS OF THE REAL 2-GRASSMANNIAN

• Jentsch Tillmann

抄録

A submanifold of a Riemannian symmetric space is called parallel if its second fundamental form is parallel. We classify parallel submanifolds of the Grassmannian G_2^+ (R^<n + 2>) which parameterizes the oriented 2-planes of the Euclidean space R^<n + 2>. Our main result states that every complete parallel submanifold of G_2^+ (R^<n + 2>), which is not a curve, is contained in some totally geodesic submanifold as a symmetric submanifold. The analogous result holds if the ambient space is the Riemannian product of two Euclidean spheres of equal curvature or the non-compact dual of one of the previously considered spaces. We also give a characterization of parallel submanifolds with curvature isotropic tangent spaces of maximal possible dimension in any symmetric space of compact or non-compact type.

収録刊行物

• Osaka Journal of Mathematics

  Osaka Journal of Mathematics 51 (2), 285-336, 2014-04

  Osaka University and Osaka City University, Departments of Mathematics

詳細情報

• CRID: 1390853649740701696
• NII論文ID: 120005422642
• NII書誌ID: AA00765910
• DOI: 10.18910/29203
• HANDLE: 11094/29203
• ISSN: 00306126
• Web Site: https://dlisv03.media.osaka-cu.ac.jp/il/meta_pub/G0000438repository_111F0000002-05102-1
• 本文言語コード: en
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