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Search: All articles in the CJM digital archive with keyword soliton

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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 metrics
Categories:53C21, 53C50, 53C25

2. CJM 1998 (vol 50 pp. 1119)

Anand, Christopher Kumar
Ward's solitons II: exact solutions
In a previous paper, we gave a correspondence between certain exact solutions to a \((2+1)\)-dimensional integrable Chiral Model and holomorphic bundles on a compact surface. In this paper, we use algebraic geometry to derive a closed-form expression for those solutions and show by way of examples how the algebraic data which parametrise the solution space dictates the behaviour of the solutions. Dans un article pr\'{e}c\'{e}dent, nous avons d\'{e}montr\'{e} que les solutions d'un mod\`{e}le chiral int\'{e}grable en dimension \( (2+1) \) correspondent aux fibr\'{e}s vectoriels holomorphes sur une surface compacte. Ici, nous employons la g\'{e}om\'{e}trie alg\'{e}brique dans une construction explicite des solutions. Nous donnons une formule matricielle et illustrons avec trois exemples la signification des invariants alg\'{e}briques pour le comportement physique des solutions.

Keywords:integrable system, chiral field, sigma model, soliton, monad, uniton, harmonic map
Category:35Q51

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