Some totally geodesic submanifolds of the nonlinear Grassmannian of a compact symmetric space

DOI10.1007/s00605-014-0642-2zbMath1304.53049OpenAlexW1964037703MaRDI QIDQ478503

Marcos Salvai

Publication date: 3 December 2014

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/11086/20321

zbMATH Keywords

geodesicsymmetric spacereflective submanifoldChow manifoldmanifold of embeddings

Mathematics Subject Classification ID

Spaces of embeddings and immersions (58D10) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Global submanifolds (53C40) Differential geometry of symmetric spaces (53C35) Compact groups (22C05) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10)

Cites Work

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• Vanishing geodesic distance for the Riemannian metric with geodesic equation the KdV-equation
• A metric on the manifold of immersions and its Riemannian curvature
• Geometry of reflective submanifolds in Riemannian symmetric spaces
• Some geometric characterizations of the Hopf fibrations of the three-sphere
• Submersions and geodesics
• Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms
• Symmetric submanifolds and generalized Gauss maps
• Sobolev metrics on diffeomorphism groups and the derived geometry of spaces of submanifolds

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