Curvature homogeneous hypersurfaces immersed in a real space form
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This article is published in Tohoku Mathematical Journal.The article was published on 1988-06-01 and is currently open access. It has received 17 citations till now. The article focuses on the topics: Curvature & Scalar curvature.read more
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A classification of Riemannian $3$-manifolds with constant principal Ricci curvatures $\rho_1=\rho_2\not=\rho_3$
TL;DR: In this article, the authors studied the topology of curvature homogeneous Riemannian spaces with dimension n = 3 and showed that curvature-homogeneous spaces are not locally homogeneous.
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On Riemannian 3-manifolds with distinct constant Ricci eigenvalues
TL;DR: For 3-dimensional Riemannian manifolds with constant Ricci eigenvalues, this article showed that the signature of the Ricci tensor is never equal to ( +, +, ) or (+,0, -).
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Curvature homogeneous spaces with a solvable Lie group as homogeneous model
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Complete k-Curvature Homogeneous Pseudo-Riemannian Manifolds
Peter B. Gilkey,Stana Nikcevic +1 more
TL;DR: For k ≥ 2, this paper showed complete k-curvature homogeneous neutral signature pseudo-Riemannian manifolds which are not locally affine homogeneous (and hence not locally homogeneous).
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Complete k-curvature homogeneous pseudo-Riemannian manifolds
Peter B. Gilkey,Stana Nikcevic +1 more
TL;DR: For any k which is at least 2, complete k-curvature homogeneous neutral signature pseudo-Riemannian manifolds which are not k+1-affine curvatures homogeneous, and hence not locally homogeneous are shown in this article.
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Cliffordalgebren und neue isoparametrische Hyperflächen
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On some types of isoparametric hypersurfaces in spheres i
Hideki Ozeki,Masaru Takeuchi +1 more
TL;DR: Theorem 2 of Part I for F = H and r = 1 is shown to be false in this paper, which implies that there are at least two types of isoparametric hypersurfaces in S with the same multiplicities; one is homogeneous, and the other is not.