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

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

2006-11-01

arxiv.org/abs/math/0611033v2

Taiwanese J. Math. Vol. 12, No. 7, (2008), 1739-1749

Mathematics

Differential Geometry

9 pages, minor corrections to terminology

Scientific paper

We 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.

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