The moduli space of left-invariant metrics of a class of six-dimensional nilpotent Lie groups

2020/11/05 by Silvio Reggiani, Francisco Vittone, Reggiani, Silvio +1
Mathematics · Physics and Astronomy · #53B35 #53C30 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2011.02854

openalex publication_date 2020/11/05 · openalex created_date 2020/11/09 · openalex updated_date 2026/07/28

Abstract

In this paper we determine the moduli space, up to isometric automorphism, of left-invariant metrics on a 6-dimensional Lie group H, such that its Lie algebra \mathfrakh admits a complex structure and has first Betti number equal to four. We also investigate which of these metrics are Hermitian and classify the corresponding complex structures.

Citations

• Complex structures on nilpotent Lie algebras
• Curvatures of left invariant metrics on lie groups
• Isometry groups of Riemannian solvmanifolds
• Almost Hermitian Geometry on Six Dimensional Nilmanifolds

Related

• The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds
• Complex structures on nilpotent Lie algebras
• Left-invariant almost para-complex structures on six-dimensional nilpotent Lie groups
• Minimal metrics on 6-dimensional complex nilmanifolds
• Automorphism group and ad-invariant metric on all six dimensional solvable real Lie algebras