• 제목/요약/키워드: conformally flat

검색결과 52건 처리시간 0.019초

LOCALLY CONFORMAL KÄHLER MANIFOLDS AND CONFORMAL SCALAR CURVATURE

  • Kim, Jae-Man
    • 대한수학회논문집
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    • 제25권2호
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    • pp.245-249
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    • 2010

  • We show that on a compact locally conformal K$\ddot{a}$hler manifold $M^{2n}$ (dim $M^{2n}\;=\;2n\;{\geq}\;4$), $M^{2n}$ is K$\ddot{a}$hler if and only if its conformal scalar curvature k is not smaller than the scalar curvature s of $M^{2n}$ everywhere. As a consequence, if a compact locally conformal K$\ddot{a}$hler manifold $M^{2n}$ is both conformally flat and scalar flat, then $M^{2n}$ is K$\ddot{a}$hler. In contrast with the compact case, we show that there exists a locally conformal K$\ddot{a}$hler manifold with k equal to s, which is not K$\ddot{a}$hler.

  • https://doi.org/10.4134/CKMS.2010.25.2.245 인용 PDF KSCI

η-Ricci Solitons in δ-Lorentzian Trans Sasakian Manifolds with a Semi-symmetric Metric Connection

  • Siddiqi, Mohd Danish
    • Kyungpook Mathematical Journal
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    • 제59권3호
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    • pp.537-562
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    • 2019

  • The aim of the present paper is to study the ${\delta}$-Lorentzian trans-Sasakian manifold endowed with semi-symmetric metric connections admitting ${\eta}$-Ricci Solitons and Ricci Solitons. We find expressions for the curvature tensor, the Ricci curvature tensor and the scalar curvature tensor of ${\delta}$-Lorentzian trans-Sasakian manifolds with a semisymmetric-metric connection. Also, we discuses some results on quasi-projectively flat and ${\phi}$-projectively flat manifolds endowed with a semi-symmetric-metric connection. It is shown that the manifold satisfying ${\bar{R}}.{\bar{S}}=0$, ${\bar{P}}.{\bar{S}}=0$ is an ${\eta}$-Einstein manifold. Moreover, we obtain the conditions for the ${\delta}$-Lorentzian trans-Sasakian manifolds with a semisymmetric-metric connection to be conformally flat and ${\xi}$-conformally flat.

  • https://doi.org/10.5666/KMJ.2019.59.3.537 인용 PDF KSCI

ON WEAKLY CYCLIC GENERALIZED B-SYMMETRIC MANIFOLDS

  • Mohabbat Ali;Aziz Ullah Khan;Quddus Khan;Mohd Vasiulla
    • 대한수학회논문집
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    • 제38권4호
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    • pp.1271-1280
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    • 2023

  • The object of the present paper is to introduce a type of non-flat Riemannian manifold, called a weakly cyclic generalized B-symmetric manifold (W CGBS)n. We obtain a sufficient condition for a weakly cyclic generalized B-symmetric manifold to be a generalized quasi Einstein manifold. Next we consider conformally flat weakly cyclic generalized B-symmetric manifolds. Then we study Einstein (W CGBS)n (n > 2). Finally, it is shown that the semi-symmetry and Weyl semi-symmetry are equivalent in such a manifold.

  • https://doi.org/10.4134/CKMS.c230032 인용 PDF

Conformally invariant tensors on hermitian manifolds

  • Matsuo, Koji
    • 대한수학회보
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    • 제33권3호
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    • pp.455-463
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    • 1996

  • In [3] and [4], Kitahara, Pak and the author obtained the conformally invariant tensor $B_0$, which is an algebraic Hermitian analogue of the Weyl conformal curvature tensor W in the Riemannian geometry, by the decomposition of the curvature tensor H of the Hermitian connection and the notion of semi-curvature-like tensors of Tanno (see[7]). In [5], the author defined a conformally invariant tensor $B_0$ on a Hermitian manifold as a modification of $B_0$. Moreover he introduced the notion of local conformal Hermitian-flatness of Hermitian manifolds and proved that the vanishing of this tensor $B_0$ together with some condition for the scalar curvatures is a necessary and sufficient condition for a Hermitian manifold to be locally conformally Hermitian-flat.

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