• Title, Summary, Keyword: semi-symmetric non-metric connection

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SEMI-RIEMANNIAN SUBMANIFOLDS OF A SEMI-RIEMANNIAN MANIFOLD WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

  • Yucesan, Ahmet;Yasar, Erol
    • Communications of the Korean Mathematical Society
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    • v.27 no.4
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    • pp.781-793
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    • 2012
  • We study some properties of a semi-Riemannian submanifold of a semi-Riemannian manifold with a semi-symmetric non-metric connection. Then, we prove that the Ricci tensor of a semi-Riemannian submanifold of a semi-Riemannian space form admitting a semi-symmetric non-metric connection is symmetric but is not parallel. Last, we give the conditions under which a totally umbilical semi-Riemannian submanifold with a semi-symmetric non-metric connection is projectively flat.

LIGHTLIKE SUBMANIFOLDS OF A SEMI-RIEMANNIAN MANIFOLD WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

  • Yucesan, Ahmet;Yasar, Erol
    • Bulletin of the Korean Mathematical Society
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    • v.47 no.5
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    • pp.1089-1103
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    • 2010
  • In this paper, we study lightlike submanifolds of a semi-Riemannian manifold admitting a semi-symmetric non-metric connection. We obtain a necessary and a sufficient condition for integrability of the screen distribution. Then we give the conditions under which the Ricci tensor of a lightlike submanifold with a semi-symmetric non-metric connection is symmetric. Finally, we show that the Ricci tensor of a lightlike submanifold of semi-Riemannian space form is not parallel with respect to the semi-symmetric non-metric connection.

ON SEMI-INVARIANT SUBMANIFOLDS OF A NEARLY KENMOTSU MANIFOLD WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

  • Ahmad, Mobin;Jun, Jae-Bok
    • Journal of the Chungcheong Mathematical Society
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    • v.23 no.2
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    • pp.257-266
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    • 2010
  • We define a semi-symmetric non-metric connection in a nearly Kenmotsu manifold and we study semi-invariant submanifolds of a nearly Kenmotsu manifold endowed with a semi-symmetric non-metric connection. Moreover, we discuss the integrability of distributions on semi-invariant submanifolds of a nearly Kenmotsu manifold with a semi-symmetric non-metric connection.

CURVATURE OF MULTIPLY WARPED PRODUCTS WITH AN AFFINE CONNECTION

  • Wang, Yong
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.5
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    • pp.1567-1586
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    • 2013
  • In this paper, we study the Einstein multiply warped products with a semi-symmetric non-metric connection and the multiply warped products with a semi-symmetric non-metric connection with constant scalar curvature, we apply our results to generalized Robertson-Walker spacetimes with a semi-symmetric non-metric connection and generalized Kasner spacetimes with a semi-symmetric non-metric connection and find some new examples of Einstein affine manifolds and affine manifolds with constant scalar curvature. We also consider the multiply warped products with an affine connection with a zero torsion.

SUBMANIFOLDS OF AN ALMOST r-PARACONTACT RIEMANNIAN MANIFOLD ENDOWED WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

  • Ahmad, Mobin;Jun, Jae-Bok
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.4
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    • pp.653-665
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    • 2009
  • We define a semi-symmetric non-metric connection in an almost r-paracontact Riemannian manifold and we consider submanifolds of an almost r-paracontact Riemannian manifold endowed with a semi-symmetric non-metric connection and obtain Gauss and Codazzi equations, Weingarten equation and curvature tensor for submanifolds of an almost r-paracontact Riemannian manifold endowed with a semi-symmetric non-metric connection.

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ON SEMI-INVARIANT SUBMANIFOLDS OF A NEARLY KENMOTSU MANIFOLD WITH A QUARTER SYMMETRIC NON-METRIC CONNECTION

  • Ahmad, Mobin;Jun, Jae-Bok
    • The Pure and Applied Mathematics
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    • v.18 no.1
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    • pp.1-11
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    • 2011
  • We define a quarter symmetric non-metric connection in a nearly Ken-motsu manifold and we study semi-invariant submanifolds of a nearly Kenmotsu manifold endowed with a quarter symmetric non-metric connection. Moreover, we discuss the integrability of the distributions on semi-invariant submanifolds of a nearly Kenmotsu manifold with a quarter symmetric non-metric connection.

LIGHTLIKE SUBMANIFOLDS OF A SEMI-RIEMANNIAN MANIFOLD WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

  • Shin, Jong Moon
    • East Asian mathematical journal
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    • v.31 no.1
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    • pp.33-40
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    • 2015
  • We study the geometry of r-lightlike submanifolds M of a semi-Riemannian manifold $\bar{M}$ with a semi-symmetric non-metric connection subject to the conditions; (a) the screen distribution of M is totally geodesic in M, and (b) at least one among the r-th lightlike second fundamental forms is parallel with respect to the induced connection of M. The main result is a classification theorem for irrotational r-lightlike submanifold of a semi-Riemannian manifold of index r admitting a semi-symmetric non-metric connection.

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

  • Jin, Dae Ho
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.2
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    • pp.619-632
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    • 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.

HALF LIGHTLIKE SUBMANIFOLDS OF A SEMI-RIEMANNIAN SPACE FORM WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

  • Jin, Dae Ho
    • The Pure and Applied Mathematics
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    • v.21 no.1
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    • pp.39-50
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    • 2014
  • In this paper, we study screen quasi-conformal irrotational half lightlike submanifolds M of a semi-Riemannian space form $\tilde{M}(c)$ admitting a semi-symmetric non-metric connection, whose structure vector field ${\zeta}$ is tangent to M. The main result is a classification theorem for such Einstein half lightlike submanifolds of a Lorentzian space form admitting a semi-symmetric non-metric connection.

ALMOST α-COSYMPLECTIC f-MANIFOLDS ENDOWED WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

  • Beyendi, Selahattin;Aktan, Nesip;Sivridag, Ali Ihsan
    • Honam Mathematical Journal
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    • v.42 no.1
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    • pp.175-185
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    • 2020
  • In this paper, we introduce almost α-Cosymplectic f-manifolds endowed with a semi-symmetric non-metric connection and give some general results concerning the curvature of such connection. In particular, we study some curvature properties of an almost α-cosymplectic f-manifold equipped with semi-symmetric non-metric connection.