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Invariants of complex structures on nilmanifolds

Edwin Alejandro Rodríguez Valencia — 2015

Archivum Mathematicum

Let $(N, J)$ be a simply connected $2 n$ -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...

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