Comparison of metrics on three-dimensional Lie groups

Federico G. Lastaria

Displaying similar documents to “Comparison of metrics on three-dimensional Lie groups”

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 $1$ .

Classification of 4-dimensional homogeneous D'Atri spaces

Teresa Arias-Marco, Oldřich Kowalski (2008)

Czechoslovak Mathematical Journal

Similarity:

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...