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1. CJM 2011 (vol 64 pp. 778)
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 metrics Categories:53C21, 53C50, 53C25 |
2. CJM 2009 (vol 61 pp. 1201)
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 manifolds Categories:53C25, 53C30 |
3. CJM 2003 (vol 55 pp. 1080)
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)
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 sums Categories:58D27, 57Q10, 57R15, 57R19, 53C20, 53C25 |