On the Ricci operator of locally homogeneous Lorentzian 3-manifolds

Giovanni Calvaruso; Oldrich Kowalski

Displaying similar documents to “On the Ricci operator of locally homogeneous Lorentzian 3-manifolds”

Classification of 4-dimensional homogeneous D'Atri spaces

Teresa Arias-Marco, Oldřich Kowalski (2008)

Czechoslovak Mathematical Journal

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The property of being a D’Atri space (i.e., a space with volume-preserving symmetries) is equivalent to the infinite number of curvature identities called the odd Ledger conditions. In particular, a Riemannian manifold $(M, g)$ satisfying the first odd Ledger condition is said to be of type $𝒜$ . The classification of all 3-dimensional D’Atri spaces is well-known. All of them are locally naturally reductive. The first attempts to classify all 4-dimensional homogeneous D’Atri spaces were done in...

Conformally flat Lorentzian three-spaces with various properties of symmetry and homogeneity

Giovanni Calvaruso (2010)

Archivum Mathematicum

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We study conformally flat Lorentzian three-manifolds which are either semi-symmetric or pseudo-symmetric. Their complete classification is obtained under hypotheses of local homogeneity and curvature homogeneity. Moreover, examples which are not curvature homogeneous are described.

A note to a theorem by K. Sekigawa

Oldřich Kowalski (1989)

Commentationes Mathematicae Universitatis Carolinae

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Riemannian manifolds in which certain curvature operator has constant eigenvalues along each helix

Yana Alexieva, Stefan Ivanov (1999)

Archivum Mathematicum

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Riemannian manifolds for which a natural skew-symmetric curvature operator has constant eigenvalues on helices are studied. A local classification in dimension three is given. In the three dimensional case one gets all locally symmetric spaces and all Riemannian manifolds with the constant principal Ricci curvatures $r_{1} = r_{2} = 0, r_{3} \neq 0$ , which are not locally homogeneous, in general.