Projects per year
Abstract
The twist construction is a method to build new interesting examples of geometric structures with torus symmetry from wellknown ones. In fact it can be used to construct arbitrary nilmanifolds from tori. In our previous paper, we presented a generalization of the twist, a shear construction of rank one, which allowed us to build certain solvable Lie algebras from R ^{n} via several shears. Here, we define the higher rank version of this shear construction using vector bundles with flat connections instead of group actions. We show that this produces any solvable Lie algebra from R ^{n} by a succession of shears. We give examples of the shear and discuss in detail how one can obtain certain geometric structures (calibrated G _{2} , cocalibrated G _{2} and almost semiKähler) on threestep solvable Lie algebras by shearing almost Abelian Lie algebras. This discussion yields a classification of calibrated G _{2} structures on Lie algebras of the form (h _{3} ⊕ R ^{3} ) ⋊ R.
Original language  English 

Journal  Geometriae Dedicata 
Volume  198 
Issue  1 
Pages (fromto)  71101 
Number of pages  31 
ISSN  00465755 
DOIs  
Publication status  Published  Feb 2019 
Keywords
 Calibrated and cocalibrated G2structures
 Generalization of twist construction
 Solvable Lie groups
Fingerprint
Dive into the research topics of 'The shear construction'. Together they form a unique fingerprint.Projects
 1 Finished

Torus symmetry and Einstein metrics
Swann, A. F. (Participant)
Independent Research Fund Denmark
01/11/2016 → 31/12/2019
Project: Research