Weakly reflective submanifolds and austere submanifolds

DOI10.2969/jmsj/06120437zbMath1187.53058arXivmath/0612384OpenAlexW2091172757MaRDI QIDQ1030018

Hiroyuki Tasaki, Osamu Ikawa, Takashi Sakai

Publication date: 1 July 2009

Published in: Journal of the Mathematical Society of Japan (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0612384

zbMATH Keywords

symmetric spaceaustere submanifold\(R\)-spacereflective submanifold\(s\)-representation

Mathematics Subject Classification ID

Global submanifolds (53C40) Differential geometry of symmetric spaces (53C35)

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Cites Work

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• On a compact Lie group acting on a manifold
• Calibrated geometries
• Critical point theory and submanifold geometry
• Minimal orbits of the isotropy groups of symmetric spaces of compact type
• Minimal Legendrian submanifolds of \(S^{2n+1}\) and absolutely area-minimizing cones
• The reflection principle for minimal submanifolds of Riemannian symmetric spaces
• A classification of hyperpolar and cohomogeneity one actions
• A General Theory of Canonical Forms
• Area-minimizing of the cone over symmetric \(R\)-spaces