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Complex curves in hypercomplex nilmanifolds with H-solvable Lie algebras
Journal of Geometry and Physics. 2023. Vol. 192. Article 104900.
Yulia Gorginyan
An operator I on a real Lie algebra is called a complex structure operator if and the -eigenspace is a Lie subalgebra in the complexification of . A hypercomplex structure on a Lie algebra is a triple of complex structures and K on satisfying the quaternionic relations. We call a hypercomplex nilpotent Lie algebra -solvable if there exists a sequence of -invariant subalgebrassuch that . We give examples of -solvable hypercomplex structures on a nilpotent Lie algebra and conjecture that all hypercomplex structures on nilpotent Lie algebras are -solvable. Let be a compact hypercomplex nilmanifold associated to an -solvable hypercomplex Lie algebra. We prove that, for a general complex structure L induced by quaternions, there are no complex curves in a complex manifold .
Publication based on the results of:
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