Displaying similar documents to “Curvature tensors in dimension four which do not belong to any curvature homogeneous space”

Curvature homogeneous spaces whose curvature tensors have large symmetries

Kazumi Tsukada (2002)

Commentationes Mathematicae Universitatis Carolinae

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We study curvature homogeneous spaces or locally homogeneous spaces whose curvature tensors are invariant by the action of “large" Lie subalgebras 𝔥 of 𝔰𝔬 ( n ) . In this paper we deal with the cases of 𝔥 = 𝔰𝔬 ( r ) ⊕ 𝔰𝔬 ( n - r ) ( 2 ≤ r ≤ n - r ) , 𝔰𝔬 ( n - 2 ) , and the Lie algebras of Lie groups acting transitively on spheres, and classify such curvature homogeneous spaces or locally homogeneous spaces.

Unit tangent sphere bundles with constant scalar curvature

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.

Surfaces with non-zero normal curvature tensor

Antonio Carlos Asperti, Dirk Ferus, Lucio Rodriguez (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Studiamo la topologia differenziale e la geometria delle superfici compatte con curvatura normale non-nulla in spazio della curvatura costante.

Curvature homogeneity of affine connections on two-dimensional manifolds

Oldřich Kowalski, Barbara Opozda, Zdeněk Vlášek (1999)

Colloquium Mathematicae

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Curvature homogeneity of (torsion-free) affine connections on manifolds is an adaptation of a concept introduced by I. M. Singer. We analyze completely the relationship between curvature homogeneity of higher order and local homogeneity on two-dimensional manifolds.