122 research outputs found
Local classification and examples of an important class of paracontact metric manifolds
We study paracontact metric -spaces with ,
equivalent to but not . In particular, we will give an alternative
proof of Theorem 3.2 of [11] and present examples of paracontact metric
-spaces and -spaces of arbitrary dimension with tensor of
every possible constant rank. We will also show explicit examples of
paracontact metric -spaces with tensor of non-constant rank,
which were not known to exist until now.Comment: 9 page
Paracontact metric manifolds without a contact metric counterpart
We study non-paraSasakian paracontact metric -spaces with
(equivalent to but ). These manifolds, which do not
have a contact geometry counterpart, will be classified locally in terms of the
rank of . We will also give explicit examples of every possible constant
rank of .Comment: 12 pages; several corrections have been made in this versio
Paracontact metric structures on the unit tangent sphere bundle
Starting from -natural pseudo-Riemannian metrics of suitable signature on
the unit tangent sphere bundle of a Riemannian manifold
, we construct a family of paracontact metric structures.
We prove that this class of paracontact metric structures is invariant under
-homothetic deformations, and classify paraSasakian and paracontact
-spaces inside this class. We also present a way to build
paracontact -spaces from corresponding contact metric structures
on .Comment: 21 page
Some Non-Compactness Results for Locally Homogeneous Contact Metric Manifolds
We exhibit some sufficient conditions ensuring the non-compactness
of a locally homogeneous, regular, contact metric manifold, under suitable
assumptions on the Jacobi operator of the Reeb vector field.
Mathematics Subject Classification. 53C25, 53C30.Universit´a degli Studi di Bari Aldo Mor
Generalized (κ, µ)-space forms and d-homothetic deformations
We study the Da-homothetic deformations of generalized (κ, µ)-
space forms. We prove that the deformed spaces are again generalized
(κ, µ)-space forms in dimension 3, but not in general, although a slight
change in their definition would make them so. We give infinitely many
examples of generalized (κ, µ)-space forms of dimension 3
The curvature tensor of almost cosymplectic and almost Kenmotsu (κ,μ,ν)-spaces
We study the Riemann curvature tensor of (κ,μ, ν)-spaces when they have almost cosymplectic and almost Kenmotsu structures, giving its writing explicitly. This leads to the definition and study of a natural generalisation of the contact metric (κ,μ, ν)-spaces. We present examples or obstruction results of these spaces in all possible cases.Ministerio de Educación, Cultura y DeporteJunta de Andalucí
Bochner and conformal flatness on normal complex contact metric manifolds
We will prove that normal complex contact metric manifolds that are Bochner flat must have constant holomorphic sectional curvature 4 and be Kähler. If they are also complete and simply connected, they must be isometric to the odd-dimensional complex projective space CP
2n+1(4) with the Fubini-Study metric. On the other hand, it is not possible for normal complex contact metric manifolds to be conformally flat
The curvature tensor of almost cosymplectic and almost Kenmotsu ( κ, μ, ν ) -space
We study the Riemann curvature tensor of (κ, µ, ν)-spaces when
they have almost cosymplectic and almost Kenmotsu structures, giving its
writing explicitly. This leads to the definition and study of a natural generalisation
of the contact metric (κ, µ, ν)-spaces. We present examples or obstruction
results of these spaces in all possible cases.Ministerio de Educación y Ciencia (MEC). EspañaPlan Andaluz de Investigación (Junta de Andalucía
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