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- W2522083676 abstract "A strictly pseudoconvex pseudo-Hermitian manifold M admits a canonical Lorentz metric as well as a canonical Riemannian metric. Using these metrics, we can define a curvaturelike function A on M. As M supports a contact form, there exists a char- acteristic vector field ~ dual to the contact structure. If ~ induces a local one-parameter group of CR transformations, then a strictly pseudoconvex pseudo-Hermitian manifold M is said to be a standard pseudo-Hermitian manifold. We study topological and geometric properties of standard pseudo-Hermitian manifolds of positive curvature A or of nonpositive curvature A. By the definition, standm-d pseudo-Hermitian manifolds are called K-contact manifolds by Sasaki. In particular, standard pseudo-Hermitian manifolds of constant cur- vature A turn out to be Sasakian space forms. It is well known that a conformaily flat manifold contains a class of Riemannian manifolds of constant curvature. A spherical CR manifold is a CR manifold whose Chern-Moser curvature form vanishes (equivalently, Weyl pseudo-conformal curvature tensor vanishes). In contrast, it is emphasized that a spherical CR manifold contains a class of standard pseudo-Hermitian manifolds of constant curvature A (i.e., Sasakian space forms). We shall classify those compact Sasakian space forms. When A ~ 0, standard pseudo-Hermitian closed aspherical manifolds are shown to be Seifert fiber spaces. We consider a deformation of standard pseudo-Hermitian structure preserving a spherical CR structure." @default.
- W2522083676 created "2016-09-30" @default.
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- W2522083676 date "1994-01-01" @default.
- W2522083676 modified "2023-09-27" @default.
- W2522083676 title "Standard Pseudo-Hermitian Structure" @default.
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