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Conformal symmetry breaking operators for anti-de Sitter spaces. (English) Zbl 1403.53081
Kielanowski, Piotr (ed.) et al., Geometric methods in physics XXXV. Workshop and summer school, Białowieża, Poland, June 26 – July 2, 2016. Cham: Birkhäuser (ISBN 978-3-319-63593-4/hbk; 978-3-319-63594-1/ebook). Trends in Mathematics, 75-91 (2018).
Summary: For a pseudo-Riemannian manifold \(X\) and a totally geodesic hypersurface \(Y\), we consider the problem of constructing and classifying all linear differential operators \(\mathcal{E}^i(X) \rightarrow\mathcal{E}^j(Y)\) between the spaces of differential forms that intertwine multiplier representations of the Lie algebra of conformal vector fields. Extending the recent results in the Riemannian setting by the authors [Conformal symmetry breaking operators for differential forms on spheres. Singapore: Springer (2016; Zbl 1353.53002)], we construct such differential operators and give a classification of them in the pseudo-Riemannian setting where both \(X\) and \(Y\) are of constant sectional curvature, illustrated by the examples of anti-de Sitter spaces and hyperbolic spaces.
For the entire collection see [Zbl 1388.00033].
Reviewer: Reviewer (Berlin)

MSC:
53Z05 Applications of differential geometry to physics
53C10 \(G\)-structures
53C20 Global Riemannian geometry, including pinching
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
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