On the classification of contact metric $(k,μ)$-spaces via tangent hyperquadric bundles

Loiudice, Eugenia; Lotta, Antonio

doi:10.48550/arxiv.1607.04082

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2019

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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%