Abstract
We prove that any simply connected \(\cal{S}\)-manifold of CR-codimension s≥ 2 is noncompact by showing that the complete, simply connected \(\cal{S}\)-manifolds are all the CR products N × {s-1} with N Sasakian, endowed with a suitable product metric. N is a Sasakian φ-symmetric space if and only if M is CR-symmetric. The locally CR-symmetric \(\cal{S}\)-manifolds are characterized by
=0 where
is the Tanaka--Webster connection. This characterization is showed to be nonvalid for nonnormal almost \(\cal{S}\)-manifolds.
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Mathematics Subject Classifications (2000). 53C25, 53C35, 32V05.
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Dileo, G., Lotta, A. On the Structure and Symmetry Properties of Almost \(\cal{S}\)-manifolds. Geom Dedicata 110, 191–211 (2005). https://doi.org/10.1007/s10711-004-2476-x
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DOI: https://doi.org/10.1007/s10711-004-2476-x