• Title/Summary/Keyword: Sasakian

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GEOMETRIC INEQUALITIES FOR SUBMANIFOLDS IN SASAKIAN SPACE FORMS

  • Presura, Ileana
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.4
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    • pp.1095-1103
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    • 2016
  • B. Y. Chen introduced a series of curvature invariants, known as Chen invariants, and proved sharp estimates for these intrinsic invariants in terms of the main extrinsic invariant, the squared mean curvature, for submanifolds in Riemannian space forms. Special classes of submanifolds in Sasakian manifolds play an important role in contact geometry. F. Defever, I. Mihai and L. Verstraelen [8] established Chen first inequality for C-totally real submanifolds in Sasakian space forms. Also, the differential geometry of slant submanifolds has shown an increasing development since B. Y. Chen defined slant submanifolds in complex manifolds as a generalization of both holomorphic and totally real submanifolds. The slant submanifolds of an almost contact metric manifolds were defined and studied by A. Lotta, J. L. Cabrerizo et al. A Chen first inequality for slant submanifolds in Sasakian space forms was established by A. Carriazo [4]. In this article, we improve this Chen first inequality for special contact slant submanifolds in Sasakian space forms.

η-RICCI SOLITONS ON TRANS-SASAKIAN MANIFOLDS WITH QUARTER-SYMMETRIC NON-METRIC CONNECTION

  • Bahadir, Oguzhan;Siddiqi, Mohd Danish;Akyol, Mehmet Akif
    • Honam Mathematical Journal
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    • v.42 no.3
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    • pp.601-620
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    • 2020
  • In this paper, firstly we discuss some basic axioms of trans Sasakian manifolds. Later, the trans-Sasakian manifold with quarter symmetric non-metric connection are studied and its curvature tensor and Ricci tensor are calculated. Also, we study the η-Ricci solitons on a Trans-Sasakian Manifolds with quartersymmetric non-metric connection. Indeed, we investigated that the Ricci and η-Ricci solitons with quarter-symmetric non-metric connection satisfying the conditions ${\tilde{R}}.{\tilde{S}}$ = 0. In a particular case, when the potential vector field ξ of the η-Ricci soliton is of gradient type ξ = grad(ψ), we derive, from the η-Ricci soliton equation, a Laplacian equation satisfied by ψ. Finally, we furnish an example for trans-Sasakian manifolds with quarter-symmetric non-metric connection admitting the η-Ricci solitons.

GENERALIZED SASAKIAN SPACE FORMS ON W0-CURVATURE TENSOR

  • Tugba Mert ;Mehmet Atceken
    • Honam Mathematical Journal
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    • v.45 no.2
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    • pp.215-230
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    • 2023
  • In this article, generalized Sasakian space forms are investigated on W0 -curvature tensor. Characterizations of generalized Sasakian space forms are obtained on W0-curvature tensor. Special curvature conditions established with the help of Riemann, Ricci, concircular, projective curvature tensors are discussed on W0-curvature tensor. With the help of these curvature conditions, important characterizations of generalized Sasakian space forms are obtained. In addition, the concepts of W0-pseudosymmetry and W0 -Ricci pseudosymmetry are defined and the behavior according to these concepts for the generalized Sasakian space form is examined.

NEARLY SASAKIAN MANIFOLD SATISFYING

  • Kim, Chong-Hon;Kim, Byong-Du
    • Bulletin of the Korean Mathematical Society
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    • v.21 no.1
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    • pp.21-26
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    • 1984
  • The notion of nearly Sasakian manifold was introduced in [1] and Z-Olszak has studied certain properties in [2] and [3]. In section (2) of this paper, we show that a nearly Sasakian manifold M admitting .GAMMA.$_{ji}$ $^{h}$ such that .del.$_{1}$ $R_{kji}$$^{h}$ =0 is of contant scalar curvature and the covariant derivate of the Ricci tensor of M is a symmetric tensor. In the last section, we shall deal with a recurrent and conformal recurrent nearly Sasakian manifold.d.

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HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE TRANS-SASAKIAN MANIFOLD WITH A QUARTER-SYMMETRIC METRIC CONNECTION

  • Jin, Dae Ho
    • East Asian mathematical journal
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    • v.33 no.5
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    • pp.543-557
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    • 2017
  • Jin [10] studied lightlike hypersurfaces of an indefinite trans-Sasakian manifold with a quarter-symmetric metric connection. We study further the geometry of this subject. The object of this paper is to study the geometry of half lightlike submanifolds of an indefinite trans-Sasakian manifold with a quarter-symmetric metric connection.

SASAKIAN STRUCTURES ON PRODUCTS OF REAL LINE AND KÄHLERIAN MANIFOLD

  • Beldjilali, Gherici;Cherif, Ahmed Mohammed;Zaga, Kaddour
    • Korean Journal of Mathematics
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    • v.27 no.4
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    • pp.1061-1075
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    • 2019
  • In this paper, we construct a Sasakian manifold by the product of real line and Kählerian manifold with exact Kähler form. This result demonstrates the close relation between Sasakian and Kählerian manifold with exact Kähler form. We present an example and an open problem.

HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE TRANS-SASAKIAN MANIFOLD OF QUASI-CONSTANT CURVATURE

  • JIN, DAE HO
    • The Pure and Applied Mathematics
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    • v.22 no.2
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    • pp.113-125
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    • 2015
  • We study half lightlike submanifolds M of an indefinite trans-Sasakian manifold of quasi-constant curvature subject to the condition that the 1-form θ and the vector field ζ, defined by (1.1), are identical with the 1-form θ and the vector field ζ of the indefinite trans-Sasakian structure { J, θ, ζ } of .