Abstract
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 $\bf R_s^{m+k}$, 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 been known for some time. A simple formula is given for obtaining these immersions from those loop group maps.
Citation
David Brander. Wayne Rossman. "A LOOP GROUP FORMULATION FOR CONSTANT CURVATURE SUBMANIFOLDS OF PSEUDO-EUCLIDEAN SPACE." Taiwanese J. Math. 12 (7) 1739 - 1749, 2008. https://doi.org/10.11650/twjm/1500405084
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