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.