Normal flows and harmonic manifolds.
González-Dávila, J.C., Vanhecke, Lieven (1997)
Publications de l'Institut Mathématique. Nouvelle Série
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González-Dávila, J.C., Vanhecke, Lieven (1997)
Publications de l'Institut Mathématique. Nouvelle Série
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Chouikha, A.Raouf (2003)
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Andrzej Derdzinski (1982)
Mathematische Annalen
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J. Cheeger, T.H. Colding (1995)
Geometric and functional analysis
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Harold Donnelly (1986)
Mathematische Zeitschrift
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Hubert Goldschmidt, Dennis DeTurck (1989)
Forum mathematicum
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Yaning Wang (2016)
Open Mathematics
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Let M3 be a three-dimensional almost Kenmotsu manifold satisfying ▽ξh = 0. In this paper, we prove that the curvature tensor of M3 is harmonic if and only if M3 is locally isometric to either the hyperbolic space ℍ3(-1) or the Riemannian product ℍ2(−4) × ℝ. This generalizes a recent result obtained by [Wang Y., Three-dimensional locally symmetric almost Kenmotsu manifolds, Ann. Polon. Math., 2016, 116, 79-86] and [Cho J.T., Local symmetry on almost Kenmotsu three-manifolds, Hokkaido...
Adam Kowalczyk (1984)
Banach Center Publications
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S. S. Singh (1983)
Annales Polonici Mathematici
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(1983)
Annales Polonici Mathematici
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Yukio Otsu (1991)
Mathematische Zeitschrift
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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.