• Title/Summary/Keyword: symmetric space

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COMPLEX SYMMETRIC WEIGHTED COMPOSITION-DIFFERENTIATION OPERATORS ON H2

  • Lian Hu;Songxiao Li;Rong Yang
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.5
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    • pp.1141-1154
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    • 2023
  • In this paper, we study the complex symmetric weighted composition-differentiation operator D𝜓,𝜙 with respect to the conjugation JW𝜉,𝜏 on the Hardy space H2. As an application, we characterize the necessary and sufficient conditions for such an operator to be normal under some mild conditions. Finally, the spectrum of D𝜓,𝜙 is also investigated.

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

  • Lee, Jae Won;Lee, Chul Woo
    • Honam Mathematical Journal
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    • v.42 no.3
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    • pp.621-643
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    • 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.

PSEUDO-PARALLEL REAL HYPERSURFACES IN COMPLEX SPACE FORMS

  • Lobos, Guillermo A.;Ortega, Miguel
    • Bulletin of the Korean Mathematical Society
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    • v.41 no.4
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    • pp.609-618
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    • 2004
  • Pseudo-parallel real hypersurfaces in complex space forms can be defined as an extrinsic analogues of pseudo-symmetric real hypersurfaces, that generalize the notion of semi-symmetric real hypersurface. In this paper a classification of the pseudo-parallel real hypersurfaces in a non-flat complex space forms is obtained.

SPACE-LIKE COMPLEX SUBMANIFOLDS OF AN INDEFINITE K HLER MANIFOLD

  • Kwon, Jung-Hwan;Pyo, Yong-Soo;Shin, Kyoung-Hwa
    • Journal of the Korean Mathematical Society
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    • v.36 no.6
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    • pp.1145-1168
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    • 1999
  • The purpose of this paper is to study the complete submanifolds with restricted space-like and time-like holomorphic bisectional curvatures in an indefinite locally symmetric K hler manifold.

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SOLITONS OF KÄHLERIAN NORDEN SPACE-TIME MANIFOLDS

  • Mundalamane, Praveena Manjappa;Shanthappa, Bagewadi Channabasappa;Siddesha, Mallannara Siddalingappa
    • Communications of the Korean Mathematical Society
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    • v.37 no.3
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    • pp.813-824
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    • 2022
  • We study solitons of Kählerian Norden space-time manifolds and Bochner curvature tensor in almost pseudo symmetric Kählerian space-time manifolds. It is shown that the steady, expanding or shrinking solitons depend on different relations of energy density/isotropic pressure, the cosmological constant, and gravitational constant.

NOTES ON THREE-DIMENSIONAL WEAKLY SYMMETRIC SPACES

  • Kurashima, Kazuo;Oguro, Takashi;Sekigawa, Kouei
    • Bulletin of the Korean Mathematical Society
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    • v.36 no.3
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    • pp.467-476
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    • 1999
  • In the present paper, we describe the action of isometry groups of 30dimensional weakly symmetric spaces and classify 3-dimensional connected weaky symmetric spaces. Further, we determine 3-dimensional weakly symmetric spaces in terms of the eigen- values of the Ricci transformation.

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

  • Jin, Dae Ho
    • Communications of the Korean Mathematical Society
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    • v.32 no.4
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    • pp.1047-1065
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    • 2017
  • The notion of a non-metric ${\phi}$-symmetric connection on semi-Riemannian manifolds was introduced by Jin [6, 7]. The object of study in this paper is generic lightlike submanifolds of an indefinite Kaehler manifold ${\bar{M}}$ with a non-metric ${\phi}$-symmetric connection. First, we provide several new results for such generic lightlike submanifolds. Next, we investigate generic lightlike submanifolds of an indefinite complex space form ${\bar{M}}(c)$ with a non-metric ${\phi}$-symmetric connection.