Curvature homogeneous spaces whose curvature tensors have large symmetries

Kazumi Tsukada

Displaying similar documents to “Curvature homogeneous spaces whose curvature tensors have large symmetries”

Curvature tensors and Singer invariants of four-dimensional homogeneous spaces

Yuki Kiyota, Kazumi Tsukada (1999)

Commentationes Mathematicae Universitatis Carolinae

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We show that the Singer invariant of a four-dimensional homogeneous space is at most $1$ .

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.

Curvature tensors in dimension four which do not belong to any curvature homogeneous space

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.

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.

Brackets and curvature. (Corchete y curvatura.)

Di Scala, Antonio J. (2005)

Revista Colombiana de Matemáticas

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