MAXIMAL NILPOTENT COMPLEX STRUCTURES

作者：Gao, Qin; Zhao, Quanting^*; Zheng, Fangyang

来源：Transformation Groups, 2023, 28(1): 241-284.

DOI：10.1007/s00031-021-09688-3

• DOLBEAULT-COHOMOLOGY
• NILMANIFOLDS
• DEFORMATIONS
• TORSION

Let the pair (g; J) be a nilpotent Lie algebra g (NLA for short) endowed with a nilpotent complex structure J. In this paper, motivated by a question in the work of Cordero, Fernandez, Gray and Ugarte [6], we prove that 2 <= nu(J) <= 3 for (g; J) when nu(g) = 2, where nu(g) is the step of g and nu(J) is the unique smallest integer such that a(J)(nu(J)) = g as in the [6, Def. 1, 8]. When nu(g) = 3, for arbitrary n >= 3, there exists a pair (g, J) such that nu(J) = dim(C) g = n, for which we call the J in the pair (g, J), satisfying nu(J) = dim(C) g = n, a maximal nilpotent (MaxN for short) complex structure. The algebraic dimension of a nilmanifold endowed with a left invariant MaxN complex structure is discussed. Furthermore, a structure theorem is proved for the pair (g; J), where nu(g) = 3 and J is a MaxN complex structure.

• 单位
  重庆师范大学