### Citations

873 | Calibrated geometries
- Harvey, Lawson
- 1982
(Show Context)
Citation Context ...g from orbits of the action of the isometry group in the symmetric space representation) is satisfied by any submanifold. The concept of a Grassmann submanifold was introduced by Harvey and Lawson in =-=[6]-=-, as follows: let ¯ N be a manifold and take any subset, V, of the Grassmann bundle over ¯ N consisting of tangential s-planes, Grs(T ¯ N) = ∪ x∈ ¯ N Grs(Tx ¯ N). A V-submanifold, N, of ¯ N, is an s-d... |

53 | Harmonic maps via Adler–Kostant–Symes theory, Harmonic maps and integrable systems
- Burstall, Pedit
- 1994
(Show Context)
Citation Context ...g a 3involution loop group, solutions of which are isometric immersions between space forms of different non-zero sectional curvature. They modified the Adler-Kostant-Symes (AKS) theory (described in =-=[4]-=-) to show how to produce many solutions by solving commuting ODEs on a finite dimensional vector space. The present author later studied this system in [1] and [3]: it had several interesting properti... |

10 | Isometric immersions of space forms and soliton theory
- Ferus, Pedit
- 1996
(Show Context)
Citation Context ...tions to a certain loop group problem were studied. The emphasis here is on the geometric interpretation of the solutions, rather than the techniques for producing solutions. In 1996, Ferus and Pedit =-=[5]-=- defined an integrable system involving a 3involution loop group, solutions of which are isometric immersions between space forms of different non-zero sectional curvature. They modified the Adler-Kos... |

9 | Curved flats, pluriharmonic maps and constant curvature immersions into pseudo-Riemannian space forms
- Brander
(Show Context)
Citation Context ...ler-Kostant-Symes (AKS) theory (described in [4]) to show how to produce many solutions by solving commuting ODEs on a finite dimensional vector space. The present author later studied this system in =-=[1]-=- and [3]: it had several interesting properties, including a relationship with pluriharmonic maps. Goal here: generalize the system to arbitrary commuting involutions of any Lie group and identify the... |

5 | Grassmann geometries in infinite dimensional homogeneous spaces and an application to reflective submanifolds
- Brander
(Show Context)
Citation Context ...nn submanifolds of infinite dimensional homogeneous spaces. In general, the associated families of special submanifolds are certain Grassmann submanifolds. An example is given from the recent article =-=[2]-=-. 1. Introduction This article discusses some of the ideas in the article [2], where solutions to a certain loop group problem were studied. The emphasis here is on the geometric interpretation of the... |

2 | A loop group formulation for constant curvature submanifolds of pseudo-Euclidean space
- Brander, Rossman
(Show Context)
Citation Context ...ant-Symes (AKS) theory (described in [4]) to show how to produce many solutions by solving commuting ODEs on a finite dimensional vector space. The present author later studied this system in [1] and =-=[3]-=-: it had several interesting properties, including a relationship with pluriharmonic maps. Goal here: generalize the system to arbitrary commuting involutions of any Lie group and identify the associa... |