Coclosed G<sub>2</sub>-structures inducing nilsolitons
Coclosed G<sub>2</sub>-structures inducing nilsolitons
Abstract We show obstructions to the existence of a coclosed <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi>G</m:mi> <m:mn>2</m:mn> </m:msub> </m:math> {\mathrm{G}_{2}} -structure on a Lie algebra <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>𝔤</m:mi> </m:math> {\mathfrak{g}} of dimension seven with non-trivial center. In particular, we prove that if there exists a Lie algebra epimorphism from <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>𝔤</m:mi> …