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Search: MSC category 53C25 ( Special Riemannian manifolds (Einstein, Sasakian, etc.) )

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1. CJM 2011 (vol 64 pp. 778)

Calvaruso, Giovanni; Fino, Anna
 Ricci Solitons and Geometry of Four-dimensional Non-reductive Homogeneous Spaces We study the geometry of non-reductive $4$-dimensional homogeneous spaces. In particular, after describing their Levi-Civita connection and curvature properties, we classify homogeneous Ricci solitons on these spaces, proving the existence of shrinking, expanding and steady examples. For all the non-trivial examples we find, the Ricci operator is diagonalizable. Keywords:non-reductive homogeneous spaces, pseudo-Riemannian metrics, Ricci solitons, Einstein-like metricsCategories:53C21, 53C50, 53C25

2. CJM 2009 (vol 61 pp. 1201)

Arvanitoyeorgos, Andreas; Dzhepko, V. V.; Nikonorov, Yu. G.
 Invariant Einstein Metrics on Some Homogeneous Spaces of Classical Lie Groups A Riemannian manifold $(M,\rho)$ is called Einstein if the metric $\rho$ satisfies the condition \linebreak$\Ric (\rho)=c\cdot \rho$ for some constant $c$. This paper is devoted to the investigation of $G$-invariant Einstein metrics, with additional symmetries, on some homogeneous spaces $G/H$ of classical groups. As a consequence, we obtain new invariant Einstein metrics on some Stiefel manifolds $\SO(n)/\SO(l)$. Furthermore, we show that for any positive integer $p$ there exists a Stiefel manifold $\SO(n)/\SO(l)$ that admits at least $p$ $\SO(n)$-invariant Einstein metrics. Keywords:Riemannian manifolds, homogeneous spaces, Einstein metrics, Stiefel manifoldsCategories:53C25, 53C30

3. CJM 2003 (vol 55 pp. 1080)

Kellerhals, Ruth
 Quaternions and Some Global Properties of Hyperbolic $5$-Manifolds We provide an explicit thick and thin decomposition for oriented hyperbolic manifolds $M$ of dimension $5$. The result implies improved universal lower bounds for the volume $\rmvol_5(M)$ and, for $M$ compact, new estimates relating the injectivity radius and the diameter of $M$ with $\rmvol_5(M)$. The quantification of the thin part is based upon the identification of the isometry group of the universal space by the matrix group $\PS_\Delta {\rm L} (2,\mathbb{H})$ of quaternionic $2\times 2$-matrices with Dieudonn\'e determinant $\Delta$ equal to $1$ and isolation properties of $\PS_\Delta {\rm L} (2,\mathbb{H})$. Categories:53C22, 53C25, 57N16, 57S30, 51N30, 20G20, 22E40

4. CJM 2001 (vol 53 pp. 780)

Nicolaescu, Liviu I.
 Seiberg-Witten Invariants of Lens Spaces We show that the Seiberg-Witten invariants of a lens space determine and are determined by its Casson-Walker invariant and its Reidemeister-Turaev torsion. Keywords:lens spaces, Seifert manifolds, Seiberg-Witten invariants, Casson-Walker invariant, Reidemeister torsion, eta invariants, Dedekind-Rademacher sumsCategories:58D27, 57Q10, 57R15, 57R19, 53C20, 53C25