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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

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.

A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries

64%

Le Donne E.

Analysis and Geometry in Metric Spaces

2017

tom 5

nr 1

116-137

Carnot groups are distinguished spaces that are rich of structure: they are those Lie groups equipped with a path distance that is invariant by left-translations of the group and admit automorphisms that are dilations with respect to the distance. We present the basic theory of Carnot groups together with several remarks.We consider them as special cases of graded groups and as homogeneous metric spaces.We discuss the regularity of isometries in the general case of Carnot-Carathéodory spaces and of nilpotent metric Lie groups.

Ograniczanie wyników

1 Analysis and Geometry in Metric Spaces

1 Complex Manifolds

1 Le Donne E.

1 Yamada T.

2 2017

Wyniki wyszukiwania

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

A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries