On the classification of contact metric ‐spaces via tangent hyperquadric bundles

Loiudice, Eugenia; Lotta, Antonio

doi:10.1002/mana.201600442

Cited by 4 publications

(2 citation statements)

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“…In the case I < −1, we obtain a new homogeneous representation of the contact metric (κ, µ) manfolds M with I M < −1, different from the Lie group representation furnished by Boeckx. Actually these models can be geometrically interpreted also as tangent hyperquadric bundle over Lorentzian space forms, as showed in [17].…”

Section: Now We Consider the Natural Decomposition Ofmentioning

confidence: 98%

Canonical fibrations of contact metric (κ,μ)-spaces

Loiudice

Lotta

2019

Pacific J. Math.

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We present a classification of the complete, simply connected, contact metric (κ, µ)-spaces as homogeneous contact metric manifolds, by studying the base space of their canonical fibration. According to the value of the Boeckx invariant, it turns out that the base is a complexification or a paracomplexification of a sphere or of a hyperbolic space. In particular, we obtain a new homogeneous representation of the contact metric (κ, µ)-spaces with Boeckx invariant less than −1. (2000): Primary 53C25, 53D10; Secondary 53C35, 53C30. Mathematics Subject Classification

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Section: Now We Consider the Natural Decomposition Ofmentioning

confidence: 98%

Canonical fibrations of contact metric (κ,μ)-spaces

Loiudice

Lotta

2019

Pacific J. Math.

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“…125-126). More recently, E. Loiudice and A. Lotta [93] showed that the tangent hyperquadric bundles T −1 M over Lorentzian space forms (M, g) of constant curvature c different from −1, equipped with a strictly pseudoconvex CR structure, also provide non equivalent examples. For these space, the formula for the Boeckx invariant changes as follows:…”

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confidence: 99%

Contact Semi-Riemannian Structures in CR Geometry: Some Aspects

Perrone

2019

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There is one-to-one correspondence between contact semi-Riemannian structures ( η , ξ , φ , g ) and non-degenerate almost CR structures ( H , ϑ , J ) . In general, a non-degenerate almost CR structure is not a CR structure, that is, in general the integrability condition for H 1 , 0 : = X - i J X , X ∈ H is not satisfied. In this paper we give a survey on some known results, with the addition of some new results, on the geometry of contact semi-Riemannian manifolds, also in the context of the geometry of Levi non-degenerate almost CR manifolds of hypersurface type, emphasizing similarities and differences with respect to the Riemannian case.

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Contact hypersurfaces and CR-symmetry

Cho

2020

Annali di Matematica

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On the classification of contact metric ‐spaces via tangent hyperquadric bundles

Abstract: We classify locally the contact metric (k,μ)‐spaces whose Boeckx invariant is ⩽−1 as tangent hyperquadric bundles of Lorentzian space forms.

Cited by 4 publications

References 16 publications

Canonical fibrations of contact metric (κ,μ)-spaces

Canonical fibrations of contact metric (κ,μ)-spaces

Contact Semi-Riemannian Structures in CR Geometry: Some Aspects

Contact hypersurfaces and CR-symmetry

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