Noncoercive differential operators on homogeneous manifolds of negative curvature and their Green functions

Roman Urban

Displaying similar documents to “Noncoercive differential operators on homogeneous manifolds of negative curvature and their Green functions”

Four-dimensional curvature homogeneous spaces

Kouei Sekigawa, Hiroshi Suga, Lieven Vanhecke (1992)

Commentationes Mathematicae Universitatis Carolinae

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We prove that a four-dimensional, connected, simply connected and complete Riemannian manifold which is curvature homogeneous up to order two is a homogeneous Riemannian space.

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

Curvature 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.