On Curvature Characterizations of Some Hypersurfaces in Spaces of Constant Curvature
Katarzyna Sawicz (2006)
Publications de l'Institut Mathématique
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Displaying similar documents to “Hypersurfaces in spaces of constant curvature satisfying some Ricci-type equations”
On Curvature Characterizations of Some Hypersurfaces in Spaces of Constant Curvature
Conditions on the conharmonic curvature tensor of Kähler hypersurfaces in complex space forms.
Dorić, M., Petrović-Torgašev, M., Verstraelen, L. (1988)
Publications de l'Institut Mathématique. Nouvelle Série
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Conditions on the Conharmonic Curvature Tensor of Kaehler Hypersurfaces in Complex Space Forms
Mirjana Đorić, Miroslava Petrović-Torgašev, L. Verstraelen (1988)
Publications de l'Institut Mathématique
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Extended Derdziński-Shen theorem for curvature tensors
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.
On semi-Riemannian manifolds satisfying some conformally invariant curvature condition
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.
Characterizations of conformally flat hypersurfaces
Johan Deprez, Piet A. Verheyen, Leopold C. A. Verstraelen (1985)
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On the equivalence of Ricci-semisymmetry and semisymmetry
Kadri Arslan, Yunus Çelik, Ryszard Deszcz, Ridvan Ezentaş (1998)
Colloquium Mathematicae
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Balkan Journal of Geometry and its Applications (BJGA)
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On generalized recurrent Kaehlerian manifolds of second order II
(1983)
Annales Polonici Mathematici
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On generalized recurrent Kaehlerian manifolds of second order I
S. S. Singh (1983)
Annales Polonici Mathematici
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Existence of metrics with harmonic curvature and non parallel Ricci tensor.
Chouikha, A.Raouf (2003)
Balkan Journal of Geometry and its Applications (BJGA)
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On some class of hypersurfaces with three distinct principal curvatures
Katarzyna Sawicz (2005)
Banach Center Publications
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We investigate hypersurfaces M in spaces of constant curvature with some special minimal polynomial of the second fundamental tensor H of third degree. We present a curvature characterization of pseudosymmetry type for such hypersurfaces. We also prove that if such a hypersurface is a manifold with pseudosymmetric Weyl tensor then it must be pseudosymmetric.