Almost contact structures and curvature tensors

Janssens, Dirk; Vanhecke, Lieven

doi:10.2996/kmj/1138036310

Cited by 218 publications

(193 citation statements)

References 29 publications

Supporting

Mentioning

188

Contrasting

Order By: Relevance

“…From Janssens and Vanhecke [11], in this paper by an almost Kenmotsu manifold we mean an almost contact metric manifold .M 2nC1 ; ; ; Á; g/ satisfying dÁ D 0 and dˆD 2Á^ˆ, where the fundamental 2-formˆof the almost contact metric manifold M 2nC1 is defined byˆ.X; Y / D g.X; Y / for any vector fields X and Y on…”

Section: Three-dimensional Almost Kenmotsu Manifoldsmentioning

confidence: 99%

Ricci solitons on almost Kenmotsu 3-manifolds

Wang

2017

Open Mathematics

View full text Add to dashboard Cite

Let .M 3 ; g/ be an almost Kenmotsu 3-manifold such that the Reeb vector field is an eigenvector field of the Ricci operator. In this paper, we prove that if g represents a Ricci soliton whose potential vector field is orthogonal to the Reeb vector field, then M 3 is locally isometric to either the hyperbolic space H 3 . 1/ or a nonunimodular Lie group equipped with a left invariant non-Kenmotsu almost Kenmotsu structure. In particular, when g represents a gradient Ricci soliton whose potential vector field is orthogonal to the Reeb vector field, then M 3 is locally isometric to either H 3 . 1/ or H 2 . 4/ R.

show abstract

Section: Three-dimensional Almost Kenmotsu Manifoldsmentioning

confidence: 99%

Ricci solitons on almost Kenmotsu 3-manifolds

Wang

2017

Open Mathematics

View full text Add to dashboard Cite

show abstract

“…Since φσ = σ, the φ-section σ is a holomorphic φ-section and the sectional curvature of a φ-section σ is called a φ-holomorphic sectional curvature (see [3], [11] and references therein for more details). If a Kenmotsu manifold M has constant φ-holomorphic sectional curvature c, then, by virtue of the Proposition 12 in [12], the Riemann curvature tensor R of M is given by, for any X, Y , Z ∈ Γ(T M ),…”

Section: Preliminariesmentioning

confidence: 99%

“…A Kenmotsu manifold is a typical example of C(α)-manifold, with α = −1, introduced by Janssens and Vanhecke [11].…”

Section: Preliminariesmentioning

confidence: 99%

Equivalence Conditions of Symmetry Properties in Lightlike Hypersurfaces of Indefinite Kenmotsu Manifolds

Lungiambudila¹,

Massamba²,

Tossa³

2016

Bulletin of the Korean Mathematical Society

View full text Add to dashboard Cite

Abstract. The paper deals with lightlike hypersurfaces which are locally symmetric, semi-symmetric and Ricci semi-symmetric in indefinite Kenmotsu manifold having constant φ-holomorphic sectional curvature c. We obtain that these hypersurfaces are totally goedesic under certain conditions. The non-existence condition of locally symmetric lightlike hypersurfaces are given. Some Theorems of specific lightlike hypersurfaces are established. We prove, under a certain condition, that in lightlike hypersurfaces of an indefinite Kenmotsu space form, tangent to the structure vector field, the parallel, semi-parallel, local symmetry, semi-symmetry and Ricci semi-symmetry notions are equivalent.

show abstract

“…Then a Sasakian manifold is a normal contact metric manifold . It is well known that the Sasakian condition may be expressed as an almost contact metric structure satisfying In particular the almost contact metric structure in this case satisfies (OXO)Y = g(ox,YX -r7(Y)¢X and an almost contact metric manifold satisfying this condition is called a Kenmotsu manifold [5,6] . Kenmotsu proved in particular the following result .…”

Section: Almost Contact Manifoldsmentioning

confidence: 99%