A strong KT (SKT) manifold consists of a Hermitian structure whose torsion three-form is closed. We classify the invariant SKT structures on four-dimensional solvable Lie groups. The classification includes solutions on groups that do not admit compact four-dimensional quotients. It also shows that there are solvable groups in dimension four that admit invariant complex structures but have no invariant SKT structure.
Classification :
53C55, 53C30, 32M10
Mots-clés :
Hermitian metric, complex structure, strong KT geometry, Kaehler with torsion, solvable Lie group
Affiliations des auteurs :
Thomas Bruun Madsen
1
;
Andrew Swann
1
1
Dept. of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark
Thomas Bruun Madsen; Andrew Swann. Invariant Strong KT Geometry on Four-Dimensional Solvable Lie Groups. Journal of Lie Theory, Tome 21 (2011) no. 1, pp. 55-70. http://geodesic.mathdoc.fr/item/JOLT_2011_21_1_a1/
@article{JOLT_2011_21_1_a1,
author = {Thomas Bruun Madsen and Andrew Swann},
title = {Invariant {Strong} {KT} {Geometry} on {Four-Dimensional} {Solvable} {Lie} {Groups}},
journal = {Journal of Lie Theory},
pages = {55--70},
year = {2011},
volume = {21},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JOLT_2011_21_1_a1/}
}
TY - JOUR
AU - Thomas Bruun Madsen
AU - Andrew Swann
TI - Invariant Strong KT Geometry on Four-Dimensional Solvable Lie Groups
JO - Journal of Lie Theory
PY - 2011
SP - 55
EP - 70
VL - 21
IS - 1
UR - http://geodesic.mathdoc.fr/item/JOLT_2011_21_1_a1/
ID - JOLT_2011_21_1_a1
ER -
%0 Journal Article
%A Thomas Bruun Madsen
%A Andrew Swann
%T Invariant Strong KT Geometry on Four-Dimensional Solvable Lie Groups
%J Journal of Lie Theory
%D 2011
%P 55-70
%V 21
%N 1
%U http://geodesic.mathdoc.fr/item/JOLT_2011_21_1_a1/
%F JOLT_2011_21_1_a1
