The Riemannian curvature tensor and differentiable spaces
Adam Kowalczyk (1984)
Banach Center Publications
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Adam Kowalczyk (1984)
Banach Center Publications
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X. Dai, G. Wie, R. Ye (1996)
Manuscripta mathematica
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M. T. K. Abbassi, Giovanni Calvaruso (2012)
Archivum Mathematicum
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We completely classify Riemannian -natural metrics of constant sectional curvature on the unit tangent sphere bundle of a Riemannian manifold . Since the base manifold turns out to be necessarily two-dimensional, weaker curvature conditions are also investigated for a Riemannian -natural metric on the unit tangent sphere bundle of a Riemannian surface.
Yu Kitabeppu, Sajjad Lakzian (2016)
Analysis and Geometry in Metric Spaces
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In this paper,we give the characterization of metric measure spaces that satisfy synthetic lower Riemannian Ricci curvature bounds (so called RCD*(K, N) spaces) with non-empty one dimensional regular sets. In particular, we prove that the class of Ricci limit spaces with Ric ≥ K and Hausdorff dimension N and the class of RCD*(K, N) spaces coincide for N < 2 (They can be either complete intervals or circles). We will also prove a Bishop-Gromov type inequality (that is ,roughly speaking,...
Oldřich Kowalski, Friedbert Prüfer (1994)
Archivum Mathematicum
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A six-parameter family is constructed of (algebraic) Riemannian curvature tensors in dimension four which do not belong to any curvature homogeneous space. Also a general method is given for a possible extension of this result.
Nicolescu, Liviu, Pripoae, Gabriel (1999)
Balkan Journal of Geometry and its Applications (BJGA)
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Mohamed Belkhelfa, Ryszard Deszcz, Małgorzata Głogowska, Marian Hotloś, Dorota Kowalczyk, Leopold Verstraelen (2002)
Banach Center Publications
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In this paper we present a review of recent results on semi-Riemannian manifolds satisfying curvature conditions of pseudosymmetry type.
Ryszard Deszcz, Wiesław Grycak (1990)
Colloquium Mathematicae
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Eric Boeckx, Lieven Vanhecke (2001)
Czechoslovak Mathematical Journal
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As a first step in the search for curvature homogeneous unit tangent sphere bundles we derive necessary and sufficient conditions for a manifold to have a unit tangent sphere bundle with constant scalar curvature. We give complete classifications for low dimensions and for conformally flat manifolds. Further, we determine when the unit tangent sphere bundle is Einstein or Ricci-parallel.
W. Roter (1977)
Colloquium Mathematicae
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