Work

The moduli space of left‐invariant metrics on six‐dimensional characteristically solvable nilmanifolds

Year: 2025

Type: article

Abstract: A real Lie algebra is said to be characteristically solvable if its derivation algebra is solvable. We explicitly determine the moduli space of left‐invariant metrics, up to isometric automorphism, for 6‐dimensional nilmanifolds whose associated Lie algebra is characteristically solvable of triangular type. We also compute the corresponding full isometry groups. For each left‐invariant metric on these nilmanifolds we compute the index and distribution of symmetry. In particular, we find the first known examples of Lie groups which do not admit a left‐invariant metric with positive index of symmetry. As an application we study the index of symmetry of nilsoliton metrics. We prove that nilsoliton metrics detect the existence of left‐invariant metrics with positive index of symmetry.

Source: Mathematische Nachrichten

DOI: 10.1002/mana.202400213

Authors: Isolda Cardoso, Ana Cosgaya, Silvio Reggiani

Institutions: National University of Rosario, Consejo Nacional de Investigaciones Científicas y Técnicas

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: Universidad Nacional de Rosario, Consejo Nacional de Investigaciones Científicas y Técnicas, Agencia Nacional de Promoción Científica y Tecnológica

Awards: G243265096, G4222307916, G7378882120