On Locally Conformally K" ahler metrics on Oeljeklaus-Toma Manifolds

2022/02/16 by Stefan Deaconu, Deaconu, Stefan, Victor Vuletescu +1 · 2 citations
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2202.08012

openalex publication_date 2022/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that Oeljeklaus-Toma manifolds X(K, U) where K is a number field of signature (s, t) such that s≥ 1, t≥ 2 and s≥ 2t admit no lck metric. Combined with the earlier results by K. Oeljeklaus - M. Toma and A. Dubickas this completely solves the problem of existence of LCK metrics on Oeljeklaus-Toma manifolds.

Cited by

• Calabi-Yau locally conformally Kähler manifolds
• Several complex structures on the Oeljeklaus-Toma manifolds

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