A loop group formulation for constant curvature submanifolds of pseudo-Euclidean space

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dc.creatorBrander, David
dc.creatorRossman, Wayne
dc.date2006-11-01
dc.date2006-11-16
dc.date.accessioned2026-07-07T10:07:33Z
dc.date.available2026-07-07T10:07:33Z
dc.descriptionWe give a loop group formulation for the problem of isometric immersions with flat normal bundle of a simply connected pseudo-Riemannian manifold $M_{c,r}^m$, of dimension $m$, constant sectional curvature $c \neq 0$, and signature $r$, into the pseudo-Euclidean space $\real_s^{m+k}$, of signature $s\geq r$. In fact these immersions are obtained canonically from the loop group maps corresponding to isometric immersions of the same manifold into a pseudo-Riemannian sphere or hyperbolic space $S_s^{m+k}$ or $H_s^{m+k}$, which have previously been studied. A simple formula is given for obtaining these immersions from those loop group maps.
dc.description9 pages, minor corrections to terminology
dc.identifierhttps://arxiv.org/abs/math/0611033
dc.identifierhttp://arxiv.org/abs/math/0611033
dc.identifierTaiwanese J. Math. Vol. 12, No. 7, (2008), 1739-1749
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/170676
dc.subjectDifferential Geometry
dc.subjectDynamical Systems
dc.subject37K25; 53C42; 53B25
dc.titleA loop group formulation for constant curvature submanifolds of pseudo-Euclidean space
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