• Title, Summary, Keyword: Sasakian 3-structure

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GENERIC SUBMANIFOLDS WITH PARALLEL MEAN CURVATURE VECTOR OF A SASAKIAN SPACE FORM

  • Ahn, Seong-Soo;Ki, U-Hang
    • Bulletin of the Korean Mathematical Society
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    • v.31 no.2
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    • pp.215-236
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    • 1994
  • The purpose of the present paper is to study generic submanifolds of a Sasakian space form with nonvanishing parallel mean curvature vector field such that the shape operator in the direction of the mean curvature vector field commutes with the structure tensor field induced on the submanifold. In .cint. 1 we state general formulas on generic submanifolds of a Sasakian manifold, especially those of a Sasakian space form. .cint.2 is devoted to the study a generic submanifold of a Sasakian manifold, which is not tangent to the structure vector. In .cint.3 we investigate generic submanifolds, not tangent to the structure vector, of a Sasakian space form with nonvanishing parallel mean curvature vactor field. In .cint.4 we discuss generic submanifolds tangent to the structure vector of a Sasakian space form and compute the restricted Laplacian for the shape operator in the direction of the mean curvature vector field. As a applications of these, in the last .cint.5 we prove our main results.

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GENERIC LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE TRANS-SASAKIAN MANIFOLD WITH AN (ℓ, m)-TYPE METRIC CONNECTION

  • Jin, Dae Ho
    • Communications of the Korean Mathematical Society
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    • v.34 no.2
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    • pp.615-632
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    • 2019
  • We study generic lightlike submanifolds M of an indefinite trans-Sasakian manifold ${\bar{M}}$ or an indefinite generalized Sasakian space form ${\bar{M}}(f_1,f_2,f_3)$ endowed with an $({\ell},m)$-type metric connection subject such that the structure vector field ${\zeta}$ of ${\bar{M}}$ is tangent to M.

INDEFINITE GENERALIZED SASAKIAN SPACE FORM ADMITTING A GENERIC LIGHTLIKE SUBMANIFOLD

  • Jin, Dae Ho
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.6
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    • pp.1711-1726
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    • 2014
  • In this paper, we study the geometry of indefinite generalized Sasakian space form $\bar{M}(f_1,f_2,f_3)$ admitting a generic lightlike submanifold M subject such that the structure vector field of $\bar{M}(f_1,f_2,f_3)$ is tangent to M. The purpose of this paper is to prove a classification theorem of such an indefinite generalized Sasakian space form.

Indefinite Generalized Sasakian Space Form Admitting a Lightlike Hypersurface

  • JIN, DAE HO
    • Kyungpook Mathematical Journal
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    • v.55 no.4
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    • pp.1097-1104
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    • 2015
  • In this paper, we study the geometry of indefinite generalized Sasakian space form $\bar{M}(f_1,f_2,f_3)$ admitting a lightlike hypersurface M subject such that the almost contact structure vector field ${\zeta}$ of $\bar{M}(f_1,f_2,f_3)$ is tangent to M. We prove a classification theorem of such an indefinite generalized Sasakian space form.

INDEFINITE TRANS-SASAKIAN MANIFOLD ADMITTING AN ASCREEN HALF LIGHTLIKE SUBMANIFOLD

  • Jin, Dae Ho
    • Communications of the Korean Mathematical Society
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    • v.29 no.3
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    • pp.451-461
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    • 2014
  • We study the geometry of indefinite trans-Sasakian manifold $\bar{M}$, of type (${\alpha},{\beta}$), admitting a half lightlike submanifold M such that the structure vector field of $\bar{M}$ does not belong to the screen and coscreen distributions of M. The purpose of this paper is to prove several classification theorems of such an indefinite trans-Sasakian manifold.

CERTAIN CLASS OF CONTACT CR-SUBMANIFOLDS OF A SASAKIAN SPACE FORM

  • Kim, Hyang Sook;Choi, Don Kwon;Pak, Jin Suk
    • Communications of the Korean Mathematical Society
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    • v.29 no.1
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    • pp.131-140
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    • 2014
  • In this paper we investigate (n+1)($n{\geq}3$)-dimensional contact CR-submanifolds M of (n-1) contact CR-dimension in a complete simply connected Sasakian space form of constant ${\phi}$-holomorphic sectional curvature $c{\neq}-3$ which satisfy the condition h(FX, Y)+h(X, FY) = 0 for any vector fields X, Y tangent to M, where h and F denote the second fundamental form and a skew-symmetric endomorphism (defined by (2.3)) acting on tangent space of M, respectively.

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

  • Jin, Dae Ho
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.3
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    • pp.1003-1022
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    • 2017
  • The object of study in this paper is generic lightlike submanifolds of an indefinite trans-Sasakian manifold with a quarter-symmetric metric connection. We study the geometry of two types of generic light-like submanifolds, which are called recurrent and Lie recurrent generic lightlike submanifolds, of an indefinite trans-Sasakian manifold with a quarter-symmetric metric connection.

ON CONTACT THREE CR SUBMANIFOLDS OF A (4m + 3)-DIMENSIONAL UNIT SPHERE

  • Kwon, Jung-Hwan;Pak, Jin--Suk
    • Communications of the Korean Mathematical Society
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    • v.13 no.3
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    • pp.561-577
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    • 1998
  • We study (n+3)-dimensional contact three CR submanifolds of a Riemannian manifold with Sasakian three structure and investigate some characterizations of $S^{4r+3}$(a) $\times$ $S^{4s+3}$(b) ($a^2$$b^2$=1, 4(r + s) = n - 3) as a contact three CR sub manifold of a (4m+3)-dimensional unit sphere.

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The structure conformal vector fields on a sasakian manifold II

  • Hyun, Jong-Ik
    • Communications of the Korean Mathematical Society
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    • v.10 no.3
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    • pp.661-679
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    • 1995
  • The concept of the structure conformal vector field C on a Sasakian manifold M is defined. The existence of such a C on M is determined by an exterior differential system in involution. In this case M is a foliate manifold and the vector field C enjoys the property to be exterior concurrent. This allows to prove some interesting properties of the Ricci tensor and Obata's theorem concerning isometries to a sphere. Different properties of the conformal Lie algebra induced by C are also discussed.

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