Nilmanifolds with a calibrated G2-structure |
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Authors: | Diego Conti |
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Affiliation: | a Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, Via Cozzi 53, 20125 Milano, Italy b Universidad del País Vasco, Facultad de Ciencia y Tecnología, Departamento de Matemáticas, Apartado 644, 48080 Bilbao, Spain |
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Abstract: | We introduce obstructions to the existence of a calibrated G2-structure on a Lie algebra g of dimension seven, not necessarily nilpotent. In particular, we prove that if there is a Lie algebra epimorphism from g to a six-dimensional Lie algebra h with kernel contained in the center of g, then h has a symplectic form. As a consequence, we obtain a classification of the nilpotent Lie algebras that admit a calibrated G2-structure. |
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Keywords: | primary, 53C38 secondary, 53C15, 17B30 |
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