退化的3-(α， δ)- sasakian流形

IF 0.5 Q3 MATHEMATICS

Complex Manifolds Pub Date : 2022-01-01 DOI:10.1515/coma-2021-0142

Oliver Goertsches, Leon Roschig, Leander Stecker

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引用次数: 1

摘要

摘要我们提出了一种在超kähler流形上构造作为Boothby-Wang丛的纤维乘积的退化3-（α，δ）-Sasakian流形的新方法。随后，我们研究了齐次退化的3-（α，δ）-Sasakian流形，并证明了不存在非平凡的紧致例子，并且证明了具有这种几何的幂零李群恰好有一个族，即四元数海森堡群。

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On Degenerate 3-(α, δ)-Sasakian Manifolds

Abstract We propose a new method to construct degenerate 3-(α, δ)-Sasakian manifolds as fiber products of Boothby-Wang bundles over hyperkähler manifolds. Subsequently, we study homogeneous degenerate 3-(α, δ)-Sasakian manifolds and prove that no non-trivial compact examples exist aswell as that there is exactly one family of nilpotent Lie groups with this geometry, the quaternionic Heisenberg groups.

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来源期刊

Complex Manifolds MATHEMATICS-

CiteScore

1.30

自引率

20.00%

发文量

审稿时长

25 weeks

期刊介绍： Complex Manifolds is devoted to the publication of results on these and related topics: Hermitian geometry, Kähler and hyperkähler geometry Calabi-Yau metrics, PDE''s on complex manifolds Generalized complex geometry Deformations of complex structures Twistor theory Geometric flows on complex manifolds Almost complex geometry Quaternionic geometry Geometric theory of analytic functions Holomorphic dynamics Several complex variables Dolbeault cohomology CR geometry.