• Title, Summary, Keyword: Lie recurrent

Search Result 7, Processing Time 0.04 seconds

REAL HYPERSURFACES IN A NON-FLAT COMPLEX SPACE FORM WITH LIE RECURRENT STRUCTURE JACOBI OPERATOR

  • Kaimakamis, George;Panagiotidou, Konstantina
    • Bulletin of the Korean Mathematical Society
    • /
    • v.50 no.6
    • /
    • pp.2089-2101
    • /
    • 2013
  • The aim of this paper is to introduce the notion of Lie recurrent structure Jacobi operator for real hypersurfaces in non-flat complex space forms and to study such real hypersurfaces. More precisely, the non-existence of such real hypersurfaces is proved.

LIGHTLIKE HYPERSURFACES OF AN INDEFINITE KAEHLER MANIFOLD WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

  • Jin, Dae Ho
    • Journal of the Korean Mathematical Society
    • /
    • v.54 no.1
    • /
    • pp.101-115
    • /
    • 2017
  • In this paper, we study three types of lightlike hypersurfaces, which are called recurrent, Lie recurrent and Hopf lightlike hypersurfaces, of an indefinite Kaehler manifold with a semi-symmetric non-metric connection. We provide several new results on such three types of lightlike hypersurfaces of an indefinite Kaehler manifold or an indefinite complex space form, with a semi-symmetric non-metric connection.

Lightlike Hypersurfaces of an Indefinite Nearly Trans-Sasakian Manifold with an (ℓ, m)-type Connection

  • Lee, Chul Woo;Lee, Jae Won
    • Kyungpook Mathematical Journal
    • /
    • v.60 no.2
    • /
    • pp.223-238
    • /
    • 2020
  • We study a lightlike hypersurface M of an indefinite nearly trans-Sasakian manifold ${\bar{M}}$ with an (ℓ, m)-type connection such that the structure vector field ζ of ${\bar{M}}$ is tangent to M. In particular, we focus on such lightlike hypersurfaces M for which the structure tensor field F is either recurrent or Lie recurrent, or such that M itself is totally umbilical or screen totally umbilical.

LIGHTLIKE HYPERSURFACES OF AN INDEFINITE KAEHLER MANIFOLD WITH A NON-METRIC 𝜙-SYMMETRIC CONNECTION

  • Jin, Dae Ho
    • Bulletin of the Korean Mathematical Society
    • /
    • v.54 no.2
    • /
    • pp.619-632
    • /
    • 2017
  • We define a new connection on semi-Riemannian manifold, which is called a non-metric ${\phi}$-symmetric connection. Semi-symmetric non-metric connection and quarter-symmetric non-metric connection are two impotent examples of this connection. The purpose of this paper is to study the geometry of lightlike hypersurfaces of an indefinite Kaehler manifold with a non-metric ${\phi}$-symmetric connection.

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

  • Jin, Dae Ho
    • Bulletin of the Korean Mathematical Society
    • /
    • v.54 no.3
    • /
    • pp.1003-1022
    • /
    • 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.

HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE KAEHLER MANIFOLD WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

  • Jin, Dae Ho
    • Communications of the Korean Mathematical Society
    • /
    • v.32 no.1
    • /
    • pp.119-133
    • /
    • 2017
  • In this paper, we study half lightlike submanifolds of an indefinite Kaehler manifold with a semi-symmetric non-metric connection. First, we characterize the geometry of two types of half lightlike submanifolds of such an indefinite Kaehler manifold. Next, we investigate the geometry of half lightlike submanifolds of an indefinite complex space form with a semi-symmetric non-metric connection.

GENERIC LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE KAEHLER MANIFOLD WITH A SEMI-SYMMETRIC METRIC CONNECTION

  • Lee, Jae Won;Lee, Chul Woo
    • Honam Mathematical Journal
    • /
    • v.42 no.3
    • /
    • pp.621-643
    • /
    • 2020
  • Depending on the characteristic vector filed ζ, a generic lightlike submanifold M in an indefinite Kaehler manifold ${\bar{M}}$ with a semi-symmetric metric connection has various characterizations. In this paper, when the characteristic vector filed ζ belongs to the screen distribution S(TM) of M, we provide some characterizations of (Lie-) recurrent generic lightlike submanifold M in an indefinite Kaehler manifold ${\bar{M}}$ with a semi-symmetric metric connection. Moreover, we characterize various generic lightlike submanifolds in an indefinite complex space form ${\bar{M}}$ (c) with a semi-symmetric metric connection.