Extending invariant complex structures
Differential Geometry
2014-06-17 v1
Abstract
We study the problem of extending a complex structure to a given Lie algebra g, which is firstly defined on an ideal h of g. We consider the next situations: h is either complex or it is totally real. The next question is to equip g with an additional structure, such as a (non)-definite metric or a symplectic structure and to ask either h is non-degenerate, isotropic, etc. with respect to this structure, by imposing a compatibility assumption. We show that this implies certain constraints on the algebraic structure of g. Constructive examples illustrating this situation are shown, in particular computations in dimension six are given.
Cite
@article{arxiv.1406.4091,
title = {Extending invariant complex structures},
author = {Rutwig Campoamor Stursberg and Isolda E. Cardoso and Gabriela P. Ovando},
journal= {arXiv preprint arXiv:1406.4091},
year = {2014}
}
Comments
22 pages, plus an Addendum