Classification of Left Invariant Riemannian metrics on Complex\n hyperbolic space

2021/06/14 by Andrijana Dekić, Dekic, Andrijana, Marijana Babic +3
Mathematics · Physics and Astronomy · #22E25 #22E60 #53C30 #58D17 #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.2106.07320

openalex publication_date 2021/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is well known that \ℂHⁿ has the structure of solvable Lie group\nwith left invariant metric of constant holomorphic sectional curvature. In this\npaper we give the full classification of all possible left invariant Riemannian\nmetrics on this Lie group. We prove that all of these metrics are of constant\nnegative scalar curvature and only one of them is Einstein (up to isometry and\nscaling). Finally, we present the relation between Ricci solitons on Heisenberg\ngroup and Einstein metric on \ℂHⁿ.\n

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