紀要論文

紀要論文

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

PARALLEL SUBMANIFOLDS OF THE REAL 2-GRASSMANNIAN

Jentsch, Tillmann

Osaka University and Osaka City University, Departments of Mathematics

英語

text

2014-04

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.

10.18910/29203

29203

PARALLEL SUBMANIFOLDS OF THE REAL 2-GRASSMANNIAN

Jentsch, Tillmann

Osaka University and Osaka City University, Departments of Mathematics

英語

2014-04

Osaka Journal of Mathematics

51

2

285

336

https://hdl.handle.net/11094/29203

10.18910/29203

https://doi.org/10.18910/29203