Special Types of Locally Conformal Closed G₂-Structures

• Main Authors: Giovanni Bazzoni, Alberto Raffero
• Format: Article
• Language: English
• Published: MDPI AG 2018-11-01
• Series: Axioms
• Subjects: locally conformal closed G₂-structure; coupled SU(3)-structure
• Online Access: https://www.mdpi.com/2075-1680/7/4/90

Motivated by known results in locally conformal symplectic geometry, we study different classes of G<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mn>2</mn> </msub> </semantics> </math> </inline-formula>-structures defined by a locally conformal closed 3-form. In particular, we provide a complete characterization of invariant exact locally conformal closed G<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mn>2</mn> </msub> </semantics> </math> </inline-formula>-structures on simply connected Lie groups, and we present examples of compact manifolds with different types of locally conformal closed G<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mn>2</mn> </msub> </semantics> </math> </inline-formula>-structures.