Authors: Dekić, Andrijana 
Babić, Marijana 
Vukmirović, Srdjan
Affiliations: Mechanics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Classification of Left Invariant Riemannian Metrics on Complex Hyperbolic Space
Journal: Mediterranean Journal of Mathematics
Volume: 19
First page: 232
Issue Date: 2022
Rank: ~M21
ISSN: 1660-5446
DOI: 10.1007/s00009-022-02152-w
Abstract: 
It is well known that CHn has the structure of a solvable Lie group with left invariant metric of constant holomorphic sectional curvature. In this paper we give the full classification of all possible left invariant Riemannian metrics on this Lie group. We prove that each of those metrics is of constant negative scalar curvature, only one of them being Einstein (up to isometry and scaling).
Keywords: Complex hyperbolic space | left invariant metric | Ricci soliton | solvmanifold
Publisher: Springer Link

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