Taiwanese Journal of Mathematics


David Brander and Wayne Rossman

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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.

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Taiwanese J. Math., Volume 12, Number 7 (2008), 1739-1749.

First available in Project Euclid: 18 July 2017

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Zentralblatt MATH identifier

Primary: 37K25: Relations with differential geometry
Secondary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42] 53B25: Local submanifolds [See also 53C40]

isometric immersions space forms loop groups


Brander, David; Rossman, Wayne. A LOOP GROUP FORMULATION FOR CONSTANT CURVATURE SUBMANIFOLDS OF PSEUDO-EUCLIDEAN SPACE. Taiwanese J. Math. 12 (2008), no. 7, 1739--1749. doi:10.11650/twjm/1500405084. https://projecteuclid.org/euclid.twjm/1500405084

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