On generalized recurrent Kaehlerian manifolds of second order II
(1983)
Annales Polonici Mathematici
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(1983)
Annales Polonici Mathematici
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Toshihiko Ikawa, Masahiro Kon (1977)
Colloquium Mathematicae
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Dussan, Martha, Noronha, Maria Helena (2005)
Balkan Journal of Geometry and its Applications (BJGA)
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Carlo Alberto Mantica, Luca Guido Molinari (2012)
Colloquium Mathematicae
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We extend a remarkable theorem of Derdziński and Shen, on the restrictions imposed on the Riemann tensor by the existence of a nontrivial Codazzi tensor. We show that the Codazzi equation can be replaced by a more general algebraic condition. The resulting extension applies both to the Riemann tensor and to generalized curvature tensors.
Zbigniew Olszak (1979)
Colloquium Mathematicae
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Pokhariyal, G.P. (2001)
Balkan Journal of Geometry and its Applications (BJGA)
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Ryszard Deszcz, Małgorzata Głogowska, Hideko Hashiguchi, Marian Hotloś, Makoto Yawata (2013)
Colloquium Mathematicae
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We investigate semi-Riemannian manifolds with pseudosymmetric Weyl curvature tensor satisfying some additional condition imposed on their curvature tensor. Among other things we prove that the so-called Roter type equation holds on such manifolds. We present applications of our results to hypersurfaces in semi-Riemannian space forms, as well as to 4-dimensional warped products.
Zbigniew Olszak (2009)
Open Mathematics
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For compact Kählerian manifolds, the holomorphic pseudosymmetry reduces to the local symmetry if additionally the scalar curvature is constant and the structure function is non-negative. Similarly, the holomorphic Ricci-pseudosymmetry reduces to the Ricci-symmetry under these additional assumptions. We construct examples of non-compact essentially holomorphically pseudosymmetric Kählerian manifolds. These examples show that the compactness assumption cannot be omitted in the above stated...
Chouikha, A.Raouf (2003)
Balkan Journal of Geometry and its Applications (BJGA)
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Mileva Prvanović (2013)
Communications in Mathematics
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By using the technique of decomposition of a Hermitian vector space under the action of a unitary group, Ganchev [2] obtained a tensor which he named the Weyl component of the antiholomorphic curvature tensor. We show that the same tensor can be obtained by direct application of the conformal change of the metric to the antiholomorphic curvature tensor. Also, we find some other conformally curvature tensors and examine some relations between them.
Kazuhiko Takano (1993)
Colloquium Mathematicae
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Andrzej Derdzinski (1980)
Mathematische Zeitschrift
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