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- 저자 : Prajjwal Pal (검색결과 3 건)
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On Almost Pseudo Conharmonically Symmetric Manifolds
Pal, Prajjwal Department of Mathematics 2014 Kyungpook mathematical journal Vol.54 No.4
The object of the present paper is to study almost pseudo conharmonically symmetric manifolds. Some geometric properties of almost pseudo conharmonically symmetric manifolds have been studied under certain curvature conditions. Finally, we give three examples of almost pseudo conharmonically symmetric manifolds.
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ON GENERALIZED Z-RECURRENT MANIFOLDS
Uday Chand De,Prajjwal Pal 한국수학교육학회 2017 純粹 및 應用數學 Vol.24 No.2
The object of the present paper is to study generalized Z-recurrent manifolds. Some geometric properties of generalized Z-recurrent manifolds have been studied under certain curvature conditions. Finally, we give an example of a generalized Z-recurrent manifold.
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Suh, Young Jin,Mantica, Carlo Alberto,De, Uday Chand,Pal, Prajjwal World Scientific 2017 INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODE Vol.14 No.9
<P>In this paper, we introduce a new tensor named <TEX>$ B$</TEX>-tensor which generalizes the <TEX>$ Z$</TEX>-tensor introduced by Mantica and Suh [Pseudo <TEX>$ Z$</TEX> symmetric Riemannian manifolds with harmonic curvature tensors, <I>Int. J. Geom. Methods Mod. Phys.</I><B>9</B>(1) (2012) 1250004]. Then, we study pseudo-<TEX>$ B$</TEX>-symmetric manifolds <TEX>$ (PBS)_{n}$</TEX> which generalize some known structures on pseudo-Riemannian manifolds. We provide several interesting results which generalize the results of Mantica and Suh [Pseudo <TEX>$ Z$</TEX> symmetric Riemannian manifolds with harmonic curvature tensors, <I>Int. J. Geom. Methods Mod. Phys.</I><B>9</B>(1) (2012) 1250004]. At first, we prove the existence of a <TEX>$ (PBS)_{n}$</TEX>. Next, we prove that a pseudo-Riemannian manifold is <TEX>$ B$</TEX>-semisymmetric if and only if it is Ricci-semisymmetric. After this, we obtain a sufficient condition for a <TEX>$ (PBS)_{n}$</TEX> to be pseudo-Ricci symmetric in the sense of Deszcz. Also, we obtain the explicit form of the Ricci tensor in a <TEX>$ (PBS)_{n}$</TEX> if the <TEX>$ B$</TEX>-tensor is of Codazzi type. Finally, we consider conformally flat pseudo-<TEX>$ B$</TEX>-symmetric manifolds and prove that a <TEX>$ (PBS)_{n}(n > 3)$</TEX> spacetime is a <TEX>$ pp$</TEX>-wave under certain conditions.</P>
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