Complex curves in hypercomplex nilmanifolds with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi mathvariant="double-struck">H</mml:mi></mml:math>-solvable Lie algebras

An operator $I$ on a real Lie algebra $A$ is called complex structure if $I^2=-Id$ and the $\sqrt{-1}$-eigenspace $A^{1,0}$ subalgebra in complexification of $A$. A hypercomplex triple structures $I,J$ $K$ satisfying quaternionic relations. We call nilpotent quaternionic-solvable there exists finite filtration by quaternionic-invariant subalgebras with commutative subquotients which converges to zero. give examples conjecture that all algebras are quaternionic-solvable. Let $(N,I,J,K)$ be compact nilmanifold associated an algebra. prove that, for general $L$ induced quaternions, no curves manifold $(N,L)$.