Ricci soliton solvmanifolds
-
Jorge Lauret
Abstract
All known examples of nontrivial homogeneous Ricci solitons are left-invariant metrics on simply connected solvable Lie groups whose Ricci operator is a multiple of the identity modulo derivations (called solsolitons, and nilsolitons in the nilpotent case). The tools from geometric invariant theory used to study Einstein solvmanifolds, turned out to be useful in the study of solsolitons as well. We prove that, up to isometry, any solsoliton can be obtained via a very simple construction from a nilsoliton N together with any abelian Lie algebra of symmetric derivations of its metric Lie algebra (đ«, ă·, ·ă). The following uniqueness result is also obtained: a given solvable Lie group can admit at most one solsoliton up to isometry and scaling. As an application, solsolitons of dimension ⊠4 are classified.
© Walter de Gruyter Berlin · New York 2011
Articles in the same Issue
- Ricci soliton solvmanifolds
- Rational normal scrolls and the defining equations of Rees algebras
- Classifications of linear operators preserving elliptic, positive and non-negative polynomials
- Graded polynomial identities and exponential growth
- Un théorÚme de la masse positive pour le problÚme de Yamabe en dimension paire
- Degenerate problems with irregular obstacles
- Twisted cyclic theory, equivariant KK-theory and KMS states
- A trace formula for varieties over a discretely valued field
Articles in the same Issue
- Ricci soliton solvmanifolds
- Rational normal scrolls and the defining equations of Rees algebras
- Classifications of linear operators preserving elliptic, positive and non-negative polynomials
- Graded polynomial identities and exponential growth
- Un théorÚme de la masse positive pour le problÚme de Yamabe en dimension paire
- Degenerate problems with irregular obstacles
- Twisted cyclic theory, equivariant KK-theory and KMS states
- A trace formula for varieties over a discretely valued field
