• Title, Summary, Keyword: Sasakian space forms

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CERTAIN RESULTS ON SUBMANIFOLDS OF GENERALIZED SASAKIAN SPACE-FORMS

  • Yadav, Sunil Kumar;Chaubey, Sudhakar K
    • Honam Mathematical Journal
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    • v.42 no.1
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    • pp.123-137
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    • 2020
  • The object of the present paper is to study certain geometrical properties of the submanifolds of generalized Sasakian space-forms. We deduce some results related to the invariant and anti-invariant slant submanifolds of the generalized Sasakian spaceforms. Finally, we study the properties of the sectional curvature, totally geodesic and umbilical submanifolds of the generalized Sasakian space-forms. To prove the existence of almost semiinvariant and anti-invariant submanifolds, we provide the non-trivial examples.

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.

BIHARMONIC CURVES IN 3-DIMENSIONAL LORENTZIAN SASAKIAN SPACE FORMS

  • Lee, Ji-Eun
    • Communications of the Korean Mathematical Society
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    • v.35 no.3
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    • pp.967-977
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    • 2020
  • In this article, we find the necessary and sufficient condition for a proper biharmonic Frenet curve in the Lorentzian Sasakian space forms 𝓜31(H) except the case constant curvature -1. Next, we find that for a slant curve in a 3-dimensional Sasakian Lorentzian manifold, its ratio of "geodesic curvature" and "geodesic torsion -1" is a constant. We show that a proper biharmonic Frenet curve is a slant pseudo-helix with 𝜅2 - 𝜏2 = -1 + 𝜀1(H + 1)𝜂(B)2 in the Lorentzian Sasakian space forms x1D4DC31(H) except the case constant curvature -1. As example, we classify proper biharmonic Frenet curves in 3-dimensional Lorentzian Heisenberg space, that is a slant pseudo-helix.

SHAPE OPERATOR OF SLANT SUBMANIFOLDS IN SASAKIAN SPACE FORMS

  • Kim, Young-Ho;Lee, Chul-Woo;Yoon, Dae-Won
    • Bulletin of the Korean Mathematical Society
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    • v.40 no.1
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    • pp.63-76
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    • 2003
  • In this article, we establish relations between the sectional curvature and the shape operator and also between the k-Ricci curvature and the shape operator for a slant submanifold in a Sasakian space form of constant $\varphi-sectional$ curvature with arbitrary codimension.