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A classification of the torsion tensors on almost contact manifolds with B-metric

Mancho Manev, Miroslava Ivanova (2014)

Open Mathematics

The space of the torsion (0,3)-tensors of the linear connections on almost contact manifolds with B-metric is decomposed in 15 orthogonal and invariant subspaces with respect to the action of the structure group. Three known connections, preserving the structure, are characterized regarding this classification.

Almost hyper-Hermitian structures in bundle spaces over manifolds with almost contact 3 -structure

Francisco Martín Cabrera (1998)

Czechoslovak Mathematical Journal

We consider almost hyper-Hermitian structures on principal fibre bundles with one-dimensional fiber over manifolds with almost contact 3-structure and study relations between the respective structures on the total space and the base. This construction suggests the definition of a new class of almost contact 3-structure, which we called trans-Sasakian, closely connected with locally conformal quaternionic Kähler manifolds. Finally we give a family of examples of hypercomplex manifolds which are not...

B.-Y. Chen's inequalities for submanifolds of Sasakian space forms

Filip Defever, Ion Mihai, Leopold Verstraelen (2001)

Bollettino dell'Unione Matematica Italiana

Recentemente, B.-Y. Chen ha introdotto una nuova serie di invarianti δ n 1 , , n k riemanniani per ogni varietà riemanniana. Ha anche ottenuto disuguaglianze strette per questi invarianti per sottovarietà di forme spaziali reali e complesse in funzione della loro curvatura media. Nel presente lavoro proviamo analoghe stime per gli invarianti δ n 1 , , n k per sottovarietà C -totalmente reali e C R di contatto di una forma spaziale di Sasaki M ~ c .

Certain contact metrics satisfying the Miao-Tam critical condition

Dhriti Sundar Patra, Amalendu Ghosh (2016)

Annales Polonici Mathematici

We study certain contact metrics satisfying the Miao-Tam critical condition. First, we prove that a complete K-contact metric satisfying the Miao-Tam critical condition is isometric to the unit sphere S 2 n + 1 . Next, we study (κ,μ)-contact metrics satisfying the Miao-Tam critical condition.

Commuting Conditions of the k-th Cho operator with the structure Jacobi operator of real hypersurfaces in complex space forms

Konstantina Panagiotidou, Juan de Dios Pérez (2015)

Open Mathematics

In this paper three dimensional real hypersurfaces in non-flat complex space forms whose k-th Cho operator with respect to the structure vector field ξ commutes with the structure Jacobi operator are classified. Furthermore, it is proved that the only three dimensional real hypersurfaces in non-flat complex space forms, whose k-th Cho operator with respect to any vector field X orthogonal to structure vector field commutes with the structure Jacobi operator, are the ruled ones. Finally, results...

Harmonic maps and Riemannian submersions between manifolds endowed with special structures

Stere Ianuş, Gabriel Eduard Vîlcu, Rodica Cristina Voicu (2011)

Banach Center Publications

It is well known that Riemannian submersions are of interest in physics, owing to their applications in the Yang-Mills theory, Kaluza-Klein theory, supergravity and superstring theories. In this paper we give a survey of harmonic maps and Riemannian submersions between manifolds equipped with certain geometrical structures such as almost Hermitian structures, contact structures, f-structures and quaternionic structures. We also present some new results concerning holomorphic maps and semi-Riemannian...

Minimal Reeb vector fields on almost Kenmotsu manifolds

Yaning Wang (2017)

Czechoslovak Mathematical Journal

A necessary and sufficient condition for the Reeb vector field of a three dimensional non-Kenmotsu almost Kenmotsu manifold to be minimal is obtained. Using this result, we obtain some classifications of some types of ( k , μ , ν ) -almost Kenmotsu manifolds. Also, we give some characterizations of the minimality of the Reeb vector fields of ( k , μ , ν ) -almost Kenmotsu manifolds. In addition, we prove that the Reeb vector field of an almost Kenmotsu manifold with conformal Reeb foliation is minimal.

On almost cosymplectic (−1, μ, 0)-spaces

Piotr Dacko, Zbigniew Olszak (2005)

Open Mathematics

In our previous paper, almost cosymplectic (κ, μ, ν)-spaces were defined as the almost cosymplectic manifolds whose structure tensor fields satisfy a certain special curvature condition. Amongst other results, it was proved there that any almost cosymplectic (κ, μ, ν)-space can be 𝒟 -homothetically deformed to an almost cosymplectic −1, μ′, 0)-space. In the present paper, a complete local description of almost cosymplectic (−1, μ, 0)-speces is established: “models” of such spaces are constructed,...

On almost cosymplectic (κ,μ,ν)-spaces

Piotr Dacko, Zbigniew Olszak (2005)

Banach Center Publications

An almost cosymplectic (κ,μ,ν)-space is by definition an almost cosymplectic manifold whose structure tensor fields φ, ξ, η, g satisfy a certain special curvature condition (see formula (eq1b)). This condition is invariant with respect to the so-called -homothetic transformations of almost cosymplectic structures. For such manifolds, the tensor fields φ, h ( = ( 1 / 2 ) ξ φ ), A ( = -∇ξ) fulfill a certain system of differential equations. It is proved that the leaves of the canonical foliation of an almost cosymplectic...

On some properties of induced almost contact structures

Zuzanna Szancer (2015)

Annales Polonici Mathematici

Real affine hypersurfaces of the complex space n + 1 with a J-tangent transversal vector field and an induced almost contact structure (φ,ξ,η) are studied. Some properties of the induced almost contact structures are proved. In particular, we prove some properties of the induced structure when the distribution is involutive. Some constraints on a shape operator when the induced almost contact structure is either normal or ξ-invariant are also given.

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