The geometry of symmetric triad and orbit spaces of Hermann actions

DOI10.2969/jmsj/06310079zbMath1213.53064OpenAlexW1983233730MaRDI QIDQ632979

Osamu Ikawa

Publication date: 28 March 2011

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

Full work available at URL: http://www.jstage.jst.go.jp/article/jmath/63/1/63_79/_article

zbMATH Keywords

symmetric spaceminimal submanifoldtotally geodesic submanifoldHermann actionaustere submanifoldsymmetric triad

Mathematics Subject Classification ID

Global submanifolds (53C40) Differential geometry of symmetric spaces (53C35) Root systems (17B22)

Related Items (14)

Biharmonic Hermitian vector bundles over compact Kähler manifolds and compact Einstein Riemannian manifolds ⋮ The (𝑀₊,𝑀₋)-method on compact symmetric spaces and its applications ⋮ Biharmonic homogeneous hypersurfaces in compact symmetric spaces ⋮ Geometric properties of orbits of Hermann actions ⋮ Harmonic maps and biharmonic maps for double fibrations of compact Lie groups ⋮ A Construction of Weakly Reflective Submanifolds in Compact Symmetric Spaces ⋮ A Duality Between Compact Symmetric Triads and Semisimple Pseudo-Riemannian Symmetric Pairs with Applications to Geometry of Hermann Type Actions ⋮ Biharmonic Homogeneous Submanifolds in Compact Symmetric Spaces ⋮ Equifocal submanifolds in a symmetric space and the infinite dimensional geometry ⋮ \(\sigma\)-actions and symmetric triads ⋮ The constancy of principal curvatures of curvature-adapted submanifolds in symmetric spaces ⋮ A duality between non-compact semisimple symmetric pairs and commutative compact semisimple symmetric triads and its general theory ⋮ Examples of austere orbits of the isotropy representations for semisimple pseudo-Riemannian symmetric spaces ⋮ The fixed point set of a holomorphic isometry, the intersection of two real forms in a Hermitian symmetric space of compact type and symmetric triads

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Collapse of the mean curvature flow for equifocal submanifolds
• Weakly reflective submanifolds and austere submanifolds
• Calibrated geometries
• Equivariant minimal immersions of compact Riemannian homogeneous spaces into compact Riemannian homogeneous spaces
• Double coset decompositions of reductive Lie groups arising from two involutions
• Minimal orbits of the isotropy groups of symmetric spaces of compact type
• Orbits of isotropy groups of compact symmetric spaces
• The reflection principle for minimal submanifolds of Riemannian symmetric spaces
• A note on M-projective modules. II
• On the geometry of the orbits of Hermann actions
• A classification of hyperpolar and cohomogeneity one actions
• Some remarks on the geometry of austere manifolds
• Orbits of Hermann actions

This page was built for publication: The geometry of symmetric triad and orbit spaces of Hermann actions