Contact hypersurfaces and CR-symmetry

Contact Metric Spaces and pseudo-Hermitian Symmetry

“…where k, µ ∈ R. [19], we know that the standard contact metric structure is Sasakian only when c = 1.) Very recently, the present author [13] proved a complete classification theorem of non-Sasakian (k, µ)-spaces which are realized as real hypersurfaces in the complex quadric Q n+1 , its dual Q * n+1 , or the complex Euclidean space C n+1 . Other remarkable properties of (k, µ)-spaces [18] are as follows:…”

Some Non-Compactness Results for Locally Homogeneous Contact Metric Manifolds

“…The simply connected, complete, non Sasakian (κ, μ)-spaces are all homogeneous and are completely classified (see [5,9,11]) and, considering two such spaces equivalent up to D a -homothetic deformations, they form a oneparameter family parametrized by R. This family contains the tangent sphere bundles T 1 S where S is a Riemannian space form. The classification relies on a result of Boeckx [5], stating that the number…”

Transversal Jacobi Operators in Almost Contact Manifolds

“…for all vector fields X and Y on the manifold. Please refer to the works in [8][9][10] for more details about almost contact structures and their associated (almost) CR structures.…”