Premium
Solvable extensions of negative Ricci curvature of filiform Lie groups
Author(s) -
Nikolayevsky Y.
Publication year - 2016
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201500019
Subject(s) - mathematics , pure mathematics , ricci curvature , lie group , lie algebra , simple lie group , extension (predicate logic) , metric (unit) , algebra over a field , curvature , geometry , computer science , programming language , operations management , economics
We give necessary and sufficient conditions of the existence of a left‐invariant metric of strictly negative Ricci curvature on a solvable Lie group the nilradical of whose Lie algebra g is a filiform Lie algebra n . It turns out that such a metric always exists, except for in the two cases, when n is one of the algebras of rank two, L n or Q n , and g is a one‐dimensional extension of n , in which cases the conditions are given in terms of certain linear inequalities for the eigenvalues of the extension derivation.