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Some relations between Hodge numbers and invariant complex structures on compact nilmanifolds

100%
Yamada T.
Complex Manifolds
|
2017
|
tom 4
|
nr 1
73-83
EN
Let N be a simply connected real nilpotent Lie group, n its Lie algebra, and € a lattice in N. If a left-invariant complex structure on N is Γ-rational, then HƏ̄s,t(Γ/N) ≃ HƏ̄s,t(nC) for each s; t. We can construct different left-invariant complex structures on one nilpotent Lie group by using the complexification and the scalar restriction. We investigate relationships to Hodge numbers of associated compact complex nilmanifolds.
2
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Transitive conformal holonomy groups

76%
Alt J.
Open Mathematics
|
2012
|
tom 10
|
nr 5
1710-1720
EN
For (M, [g]) a conformal manifold of signature (p, q) and dimension at least three, the conformal holonomy group Hol(M, [g]) ⊂ O(p + 1, q + 1) is an invariant induced by the canonical Cartan geometry of (M, [g]). We give a description of all possible connected conformal holonomy groups which act transitively on the Möbius sphere S p,q, the homogeneous model space for conformal structures of signature (p, q). The main part of this description is a list of all such groups which also act irreducibly on ℝp+1,q+1. For the rest, we show that they must be compact and act decomposably on ℝp+1,q+1, in particular, by known facts about conformal holonomy the conformal class [g] must contain a metric which is either Einstein (if p = 0 or q = 0) or locally isometric to a so-called special Einstein product.
3
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On the Ricci operator of locally homogeneous Lorentzian 3-manifolds

76%
Calvaruso G., Kowalski O.
Open Mathematics
|
2009
|
tom 7
|
nr 1
124-139
EN
We determine the admissible forms for the Ricci operator of three-dimensional locally homogeneous Lorentzian manifolds.
4
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A non-homogeneous, symmetric contact projective structure

76%
Zalabová L.
Open Mathematics
|
2014
|
tom 12
|
nr 6
879-886
EN
We construct a non-homogeneous contact projective structure which is symmetric from the point of view of parabolic geometries.
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