Examples of a generalization of contact metric structures on fibre bundles

Terlizzi, Luigia Di; Konderak, Jerzy J.

doi:10.1007/s00022-007-1915-x

Cited by 8 publications

(11 citation statements)

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“…The manifold U (2) is compact, connected, with Euler number χ(U (2)) = 0, thus we can define a left-invariant Lorentz metric g such that the vector fields ξ 1 , ξ 2 , X and Y form an orthonormal basis with g(ξ 1 , ξ 1 ) = −1. Such a structure on U (2) is constructed in the Riemannian context ( [11]) and then it is adapted to the Lorentzian case ( [7]).…”

Section: Null Osserman Condition and Lorentz S-manifoldsmentioning

confidence: 99%

An Osserman-type condition on g.f.f-manifolds with Lorentz metric

Brunetti

2014

Ann. Polon. Math.

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A condition of Osserman type, called ϕ-null Osserman condition, is introduced and studied in the context of Lorentz globally framed f -manifolds. An explicit example shows the naturalness of this condition in the setting of Lorentz S-manifolds. We prove that a Lorentz S-manifold with constant ϕ-sectional curvature is ϕ-null Osserman, extending a result stated for Lorentz Sasaki space forms. Then we state a characterization for a particular class of ϕ-null Osserman S-manifolds. Finally, some examples are examined.2000 Mathematics Subject Classification. 53C25, 53C50, 53B30.

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Section: Null Osserman Condition and Lorentz S-manifoldsmentioning

confidence: 99%

An Osserman-type condition on g.f.f-manifolds with Lorentz metric

Brunetti

2014

Ann. Polon. Math.

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“…In particular, from (3) we see that E is integrable, hence it defines a foliation £ of M. Therefore we can regard an r-contact manifold as a smooth manifold of dimension 2n + r foliated by an r-dimensional foliation and whose transverse geometry is modelled on a symplectic manifold. We remark that, as pointed out in [9], there are examples of (2n+r)-dimensional smooth manifolds, with r even, which admits an r-contact structure but no symplectic structures, and (2n + r)-dimensional smooth manifolds, with r odd, which admits an r-contact structure but no contact structures.…”

Section: A Generalization Of Contact Manifoldsmentioning

confidence: 54%

INTEGRAL SUB MANIFOLDS OF r-CONTACT MANIFOLDS

Montano¹

2008

Demonstratio Mathematica

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Abstract.We study the properties of integral submanifolds of the contact distribution of an r-contact manifold. In particular we find relations between them, rcontactomorphisms and r-contact vector fields, and we find some results for integral submanifolds of defined by {771 = 0,..., r} r = 0} -the contact distribution of (M 2n+r , 771,..., r]r) -is as far from being integrable as possible. An integral submanifold of (the contact distribution of) M 2n+r is by definition a submanifold M s of M 2n+r such that any vector tangent to M s belongs to the distribution V. In this case s < n and when s -n the n-dimensional integral submanifold in question is called a Legendrian submanifold.In this work we find some properties of integral submanifolds and relate them with r-contactomorphisms and r-contact vector fields. Some of these properties are a consequence of a Darboux theorem for r-contact manifold, which we prove in §2. Next, we study the immersion of integral submanifolds into the ambient space endowed with a compatible metric /-structure. In particular, we concentrate our attention on Legendrian submanifolds of «S-space forms, finding conditions -in terms of sectional curvature, Ricci curvature or scalar curvature -which ensure that a minimal Legendrian submanifold of an 5-space form is totally geodesic.1991 Mathematics Subject Classification: 53C12, 53C15.

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“…It is known that U (2) does not admit a Kähler or a symplectic structure; namely, (cf. [8]), its Betti numbers are…”

Section: Proposition 35 the Harmonicity Of Vector Fields Is Invariamentioning

confidence: 99%

“…In [8], it is shown that if s is even, s = 2t, then b 1 is odd, which implies that E 2n+2t cannot carry a Kähler structure for any values n, t ∈ N * . In fact, the first Betti number of…”

Section: Example 32 ([1 8])mentioning

confidence: 99%

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HARMONIC AND HOLOMORPHIC VECTOR FIELDS ON AN Ƒ-Manifold WITH PARALLELIZABLE KERNEL

Terlizzi¹,

Pastore²,

Wolak³

2014

Annals of the Alexandru Ioan Cuza University - Mathematics

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We consider a natural generalization of the metric almost contact manifolds that we call metric f.pk-manifolds. They are Riemannian manifolds with a compatible f -structure which admits a parallelizable kernel. With some additional conditions they are called S-manifolds. We give some examples and study some properties of harmonic 1-forms on such manifolds. We also study harmonicity and holomorphicity of vector fields on them.Mathematics Subject Classification 2010: 53C15, 53C25.

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Examples of a generalization of contact metric structures on fibre bundles

Cited by 8 publications

References 11 publications

An Osserman-type condition on g.f.f-manifolds with Lorentz metric

An Osserman-type condition on g.f.f-manifolds with Lorentz metric

INTEGRAL SUB MANIFOLDS OF r-CONTACT MANIFOLDS

HARMONIC AND HOLOMORPHIC VECTOR FIELDS ON AN Ƒ-Manifold WITH PARALLELIZABLE KERNEL

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