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On a class of twistorial maps. (English) Zbl 1149.53028
Summary: We show that a natural class of twistorial maps gives a pattern for apparently different geometric maps, such as, (1,1)-geodesic immersions from (1,2)-symplectic almost Hermitian manifolds and pseudo horizontally conformal submersions with totally geodesic fibres for which the associated almost CR-structure is integrable. Along the way, we construct for each constant curvature Riemannian manifold \((M,g)\), of dimension \(m\), a family of twistor spaces \(\{Z_r (M)\}_{1\leqslant r< \frac {1}{2} m}\) such that \(Z_r(M)\) parametrizes naturally the set of pairs \((P,J)\), where \(P\) is a totally geodesic submanifold of \((M,g)\), of codimension \(2r\), and \(J\) is an orthogonal complex structure on the normal bundle of \(P\) which is parallel with respect to the normal connection.

53C28 Twistor methods in differential geometry
53C43 Differential geometric aspects of harmonic maps
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