• 제목/요약/키워드: Conharmonically flat

검색결과 7건 처리시간 0.022초

CONHARMONICALLY FLAT FIBRED RIEMANNIAN SPACE II

  • Lee, Sang-Deok;Kim, Byung-Hak
    • Journal of applied mathematics & informatics
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    • 제9권1호
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    • pp.441-447
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    • 2002
  • We show that the conharmonical1y flat K-contact find cosymplectic manifolds are local1y Euclidean. Evidently non locally Euclidean conharmonically flat Sasakian manifold does not exist. Moreover we see that conharmonically flat Kenmotsu manifold does not exist and conharmonically flat fibred quasi quasi Sasakian space is locally Euclidean if and only if the scalar curvature of each fibre vanishes identically.

REMARKS ON CONFORMAL TRANSFORMATION ON RIEMANNIAN MANIFOLDS

  • Kim, Byung-Hak;Choi, Jin-Hyuk;Lee, Young-Ok
    • Journal of applied mathematics & informatics
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    • 제27권3_4호
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    • pp.857-864
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    • 2009
  • The special conformally flatness is a generalization of a sub-projective space. B. Y. Chen and K. Yano ([4]) showed that every canal hypersurface of a Euclidean space is a special conformally flat space. In this paper, we study the conditions for the base space B is special conformally flat in the conharmonically flat warped product space $B^n{\times}f\;R^1$.

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ON SPECIAL CONFORMALLY FLAT SPACES WITH WARPED PRODUCT METRICS

  • Kim, Byung-Hak;Lee, Sang-Deok;Choi, Jin-Hyuk;Lee, Young-Ok
    • Journal of applied mathematics & informatics
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    • 제29권1_2호
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    • pp.497-504
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    • 2011
  • In 1973, B. Y. Chen and K. Yano introduced the special conformally flat space for the generalization of a subprojective space. The typical example is a canal hypersurface of a Euclidean space. In this paper, we study the conditions for the base space B to be special conformally flat in the conharmonically flat warped product space $B^n{\times}_fR^1$. Moreover, we study the special conformally flat warped product space $B^n{\times}_fF^p$ and characterize the geometric structure of $B^n{\times}_fF^p$.

FIBRED RIEMANNIAN SPACE AND INFINITESIMAL TRANSFORMATION

  • Kim, Byung-Hak;Choi, Jin-Hyuk
    • Journal of applied mathematics & informatics
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    • 제24권1_2호
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    • pp.541-545
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    • 2007
  • In this paper, we study the infinitesimal transformation on the fibred Riemannian space. The conharmonic curvature tensor is invariant under the conharmonic transformation. We have proved that the conharmonically flat fibred Riemannian space with totally geodesic fibre is locally the Riemannian product of the base space and a fibre.

A Class of Lorentzian α-Sasakian Manifolds

  • Yildiz, Ahmet;Turan, Mine;Murathan, Cengizhan
    • Kyungpook Mathematical Journal
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    • 제49권4호
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    • pp.789-799
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    • 2009
  • In this study we consider ${\varphi}$-conformally flat, ${\varphi}$-conharmonically flat, ${\varphi}$-projectively at and ${\varphi}$-concircularly flat Lorentzian ${\alpha}$-Sasakian manifolds. In all cases, we get the manifold will be an ${\eta}$-Einstein manifold.

ON TWISTED PRODUCT MANIFOLD WITH CONHARMONICALLY FLAT

  • Oh, Won-Tae;Lee, Young-Ok
    • Journal of applied mathematics & informatics
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    • 제11권1_2호
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    • pp.385-390
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    • 2003
  • In this paper, we are going to study the twisted product manifold in connection with conharmonic transformation.