Construction of LCS and LCK structures on Lie algebras and solvmanifolds. (arXiv:1811.12266v1 [math.DG])

We show a method to build new examples of Lie algebras admitting LCS or LCK structures starting with a smaller dimensional Lie algebra endowed with a LCS or LCK structure respectively, and a suitable representation. We also study the existence of lattices in the associated simply connected Lie groups in order to obtain compact examples of manifolds admitting these kind of structures. Finally we show that the Lie algebra underlying of the well known Oeljesklaus-Toma solvmanifold can me reobtained using our construction. 查看全文>>