Work

Nilmanifolds with non-nilpotent complex structures and their pseudo-Kähler geometry

Year: 2025

Type: article

Abstract: We classify nilpotent Lie algebras with complex structures of weakly non-nilpotent type in real dimension eight, which is the lowest dimension where they arise. Our study, together with previous results on strongly non-nilpotent structures, completes the classification of 8-dimensional nilpotent Lie algebras admitting complex structures of non-nilpotent type. As an application, we identify those that support a pseudo-Kähler metric, thus providing new counterexamples to a previous conjecture and an infinite family of (Ricci-flat) non-flat neutral Calabi–Yau structures. Moreover, we arrive at the topological restriction $$b_1(X)\ge 3$$ b 1 ( X ) ≥ 3 for every pseudo-Kähler nilmanifold X with an invariant complex structure, up to complex dimension four.

Source: Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas

DOI: 10.1007/s13398-025-01712-5

Authors: Adela Latorre, Luis Ugarte

Institutions: Universidad Politécnica de Madrid, Universidad de Zaragoza

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,390

Funders: Gobierno de Aragón, Agencia Estatal de Investigación