The local structure of trans-Sasakian manifolds

Marrero, Juan Carlos

doi:10.1007/bf01760000

Cited by 115 publications

(119 citation statements)

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“…If both α and β vanish, then M is a cosymplectic manifold. Actually, in [6], Marrero showed that a trans-Sasakian manifold of dimension greater than or equal to 5 is either α-Sasakian, β-Kenmotsu or cosymplectic.…”

Section: Preliminariesmentioning

confidence: 99%

Generalized Sasakian-space-forms

2004

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Section: Preliminariesmentioning

confidence: 99%

Generalized Sasakian-space-forms

2004

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“…In ( [7]) the author proved that a trans-Sasakian manifold of dimension ≥ 5 is either α-Sasakian or β-Kenmotsu manifold. Trans-Sasakian manifolds of dimension 3 are also classified in ( [7]).…”

Section: Results Of the Papermentioning

confidence: 99%

“…Trans-Sasakian manifolds of dimension 3 are also classified in ( [7]). In our paper we obtain some examples of 3-dimensional trans-Sasakian structures which are neither of class C 5 nor C 6 .…”

Section: Results Of the Papermentioning

confidence: 99%

On D-homothetic deformation of trans-Sasakian structure

Shaikh¹,

Baishya²,

Eyasmin³

2008

Demonstratio Mathematica

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Abstract. The object of the present paper is to study a transformation called Dhomothetic deformation of trans-Sasakian structure. Among others it is shown that in a trans-Sasakian manifold, the Ricci operator Q does not commute with the structure tensor φ and the operator Qφ − φQ is conformal under a D-homothetic deformation. Also the φ-sectional curvature of a trans-Sasakian manifold is conformal under such a deformation. Some non-trivial examples of trans-Sasakian (non-Sasakian) manifolds with global vector fields are obtained. IntroductionA. Trans-Sasakian structure Let V be a 2n-dimensional C ∞ -almost Hermitian manifold with metric g and almost complex structure J. The Kähler form Ω is defined by Ω(X, Y ) = g(X, JY ) for all X, Y ∈ χ(V ), χ(V ) being the Lie algebra of C ∞ vector fields on V . Then V is said to be Kähler if dΩ = 0 and N J = 0, where N J denotes Nijenhuis tensor of J. Also V is called locally conformal Kähler if its metric is conformally related to a Kähler metric in some neighbourhood of every point of V .Let M be a (2n+1)-dimensional C ∞ -almost contact metric manifold with metric g and almost contact metric structure (φ, ξ, η, g). Then we have (1.1)for X, Y ∈ χ(M ), where I denotes the identity transformation and ⊗ denotes the tensor product. The fundamental 2-form Φ of the almost contact metric 1991 Mathematics Subject Classification: 53C15, 53C25.

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“…The class 6 5 ( [10,11]) coincides with the class of the trans-Sasakian structures of type (α, β). In fact, in [11], local nature of the two subclasses, namely, C 5 and C 6 structures of trans-Sasakian structures are characterized completely.…”

Section:   mentioning

confidence: 95%