Invariants of complex structures on nilmanifolds

Rodríguez Valencia, Edwin Alejandro. "Invariants of complex structures on nilmanifolds." Archivum Mathematicum 051.1 (2015): 27-50. <http://eudml.org/doc/270053>.

@article{RodríguezValencia2015,
abstract = {Let $(N, J)$ be a simply connected $2n$-dimensional nilpotent Lie group endowed with an invariant complex structure. We define a left invariant Riemannian metric on $N$ compatible with $J$ to be minimal, if it minimizes the norm of the invariant part of the Ricci tensor among all compatible metrics with the same scalar curvature. In [7], J. Lauret proved that minimal metrics (if any) are unique up to isometry and scaling. This uniqueness allows us to distinguish two complex structures with Riemannian data, giving rise to a great deal of invariants. We show how to use a Riemannian invariant: the eigenvalues of the Ricci operator, polynomial invariants and discrete invariants to give an alternative proof of the pairwise non-isomorphism between the structures which have appeared in the classification of abelian complex structures on 6-dimensional nilpotent Lie algebras given in [1]. We also present some continuous families in dimension 8.},
author = {Rodríguez Valencia, Edwin Alejandro},
journal = {Archivum Mathematicum},
keywords = {complex; nilmanifolds; nilpotent Lie groups; minimal metrics; Pfaffian forms; complex; nilmanifolds; nilpotent Lie groups; minimal metrics; Pfaffian forms},
language = {eng},
number = {1},
pages = {27-50},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Invariants of complex structures on nilmanifolds},
url = {http://eudml.org/doc/270053},
volume = {051},
year = {2015},
}

TY - JOUR
AU - Rodríguez Valencia, Edwin Alejandro
TI - Invariants of complex structures on nilmanifolds
JO - Archivum Mathematicum
PY - 2015
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 051
IS - 1
SP - 27
EP - 50
AB - Let $(N, J)$ be a simply connected $2n$-dimensional nilpotent Lie group endowed with an invariant complex structure. We define a left invariant Riemannian metric on $N$ compatible with $J$ to be minimal, if it minimizes the norm of the invariant part of the Ricci tensor among all compatible metrics with the same scalar curvature. In [7], J. Lauret proved that minimal metrics (if any) are unique up to isometry and scaling. This uniqueness allows us to distinguish two complex structures with Riemannian data, giving rise to a great deal of invariants. We show how to use a Riemannian invariant: the eigenvalues of the Ricci operator, polynomial invariants and discrete invariants to give an alternative proof of the pairwise non-isomorphism between the structures which have appeared in the classification of abelian complex structures on 6-dimensional nilpotent Lie algebras given in [1]. We also present some continuous families in dimension 8.
LA - eng
KW - complex; nilmanifolds; nilpotent Lie groups; minimal metrics; Pfaffian forms; complex; nilmanifolds; nilpotent Lie groups; minimal metrics; Pfaffian forms
UR - http://eudml.org/doc/270053
ER -