Weakly reflective submanifolds and austere submanifolds

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概要

• 論文の詳細を見る

• An austere submanifold is a minimal submanifold where for each normal vector, the set of eigenvalues of its shape operator is invariant under the multiplication by −1. In the present paper, we introduce the notion of weakly reflective submanifold, which is an austere submanifold with a reflection for each normal direction, and study its fundamental properties. Using these, we determine weakly reflective orbits and austere orbits of linear isotropy representations of Riemannian symmetric spaces.

• 社団法人 日本数学会の論文
• 2009-04-01

著者

• Ikawa Osamu

  Department Of General Education Fukushima National College Of Technology

• Tasaki Hiroyuki

  Graduate School Of Pure And Applied Science University Of Tsukuba

• SAKAI Takashi

  Graduate School of Science Osaka City University

関連論文

• Totally geodesic submanifolds of maximal rank in symmetric spaces
• Harmonic mappings, minimal and totally geodesic immersions of compact Riemannian homogeneous spaces into Grassmann manifolds.
• The geometry of symmetric triad and orbit spaces of Hermann actions
• Weakly reflective submanifolds and austere submanifolds
• Geometry of reflective submanifolds in Riemannian symmetric spaces

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