On the standard nondegenerate almost CR structure of tangent hyperquadric bundles

Perrone, Domenico

doi:10.1007/s10711-016-0167-z

Cited by 5 publications

(9 citation statements)

References 20 publications

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“…where varies in ℝ⧵{−1}, so that for ⩽ 0, these examples cover all possible values of the Boeckx invariant in (−∞, −1]. We remark that, as in the Riemannian case, −1 is again a strictly pseudo-convex hypersurface of ( , ) (see also [14] for a recent study of these manifolds from the point of view of geometry). However, in this case the Webster metric is no longer a scalar multiple of the (semi-Riemannian) Sasaki metric of .…”

Section: Introductionmentioning

confidence: 90%

“…Moreover, being

d_{p} f = L

, we have

{(d F)}_{t} |_{H_{t} false(T_{- 1} M false)} = - I d,

and thus F is a local

C R

symmetry at t . Vice versa, if

T_{- 1} M

is a locally symmetric pseudo‐Hermitian manifold, then in particular

(H true(T_{- 1} M true), J)

is a

C R

structure and hence, by [, Theorem 1],

(M, g)

has constant sectional curvature.

□

…”

Section: Contact Metric (Kμ)‐structures On Tangent Hyperquadric Bundlesmentioning

confidence: 99%

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

Loiudice

Lotta

2018

Mathematische Nachrichten

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Section: Introductionmentioning

confidence: 90%

“…Moreover, being

d_{p} f = L

, we have

{(d F)}_{t} |_{H_{t} false(T_{- 1} M false)} = - I d,

and thus F is a local

C R

symmetry at t . Vice versa, if

T_{- 1} M

is a locally symmetric pseudo‐Hermitian manifold, then in particular

(H true(T_{- 1} M true), J)

is a

C R

structure and hence, by [, Theorem 1],

(M, g)

has constant sectional curvature.

□

…”

Section: Contact Metric (Kμ)‐structures On Tangent Hyperquadric Bundlesmentioning

confidence: 99%

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

Loiudice

Lotta

2018

Mathematische Nachrichten

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“…First, we recall few notions of almost CR structures (see [11,15,17] Then we have the following: Proposition 6.1. For an almost CR structure (H(M ), J, θ), the following statements are equivalent :…”

Section: Almost Cr Structuresmentioning

confidence: 99%

Certain results on almost contact pseudo-metric manifolds

2019

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We study the geometry of almost contact pseudo-metric manifolds in terms of tensor fields h := 1 2 £ ξ ϕ and ℓ := R(·, ξ)ξ, emphasizing analogies and differences with respect to the contact metric case. Certain identities involving ξ-sectional curvatures are obtained. We establish necessary and sufficient condition for a nondegenerate almost CR structure (H(M ), J, θ) corresponding to almost contact pseudo-metric manifold M to be CR manifold. Finally, we prove that a contact pseudometric manifold (M, ϕ, ξ, η, g) is Sasakian if and only if the corresponding nondegenerate almost CR structure (H(M ), J) is integrable and J is parallel along ξ with respect to the Bott partial connection.Mathematics Subject Classification (2010). 53C15; 53C25; 53D10.

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“…where π is the usual projection π : TM → H. The generalized Tanaka-Webster connection∇ is due to Tanno [20] (though confined to the positive definite case). For a nondegenerate almost CR manifold,∇ was considered in [47,48].∇ admits an axiomatic description similar to that of the ordinary Tanaka-Webster connection (cf. Tanaka [10]) except for the property∇ϕ = 0.…”

Section: The (Generalized) Tanaka-webster Connection and The Pseudohementioning

confidence: 99%

“…The pseudohermitian scalar curvaturer is also called the (generalized) Tanaka-Webster scalar curvature [20]. In [48] we considered the following Definition 5. A nondegenerate almost CR manifold (M, H, J, θ), dim M = (2n + 1), is said to be pseudo-Einstein if the pseudohermitian Ricci tensorRic is proportional to the Levi form, that is,Ric |H = λL θ , where λ =r/2n.…”

Section: The (Generalized) Tanaka-webster Connection and The Pseudohementioning

confidence: 99%

Contact Semi-Riemannian Structures in CR Geometry: Some Aspects

Perrone

2019

Axioms

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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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On the standard nondegenerate almost CR structure of tangent hyperquadric bundles

Cited by 5 publications

References 20 publications

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

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

Certain results on almost contact pseudo-metric manifolds

Contact Semi-Riemannian Structures in CR Geometry: Some Aspects

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