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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