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Displaying similar documents to “Classification of Certain Compact Riemannian Manifolds with Harmonic Curvature and Non-parallel Ricci Tensor.”

A class of 3-dimensional almost Kenmotsu manifolds with harmonic curvature tensors

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...

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.