Curvature homogeneity of affine connections on two-dimensional manifolds

Oldřich Kowalski; Barbara Opozda; Zdeněk Vlášek

Displaying similar documents to “Curvature homogeneity of affine connections on two-dimensional manifolds”

Curvature homogeneous spaces whose curvature tensors have large symmetries

Kazumi Tsukada (2002)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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 $𝔥 = 𝔰𝔬 (r) \oplus 𝔰𝔬 (n - r)$ $(2 \leq r \leq n - r)$ , $𝔰𝔬 (n - 2)$ , and the Lie algebras of Lie groups acting transitively on spheres, and classify such curvature homogeneous spaces or locally homogeneous spaces.

Curvature tensors and Singer invariants of four-dimensional homogeneous spaces

Yuki Kiyota, Kazumi Tsukada (1999)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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

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

Oldřich Kowalski, Friedbert Prüfer (1994)

Archivum Mathematicum

Similarity:

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

Similarity:

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.