规则萨萨基流形上的投影诱导凯勒锥

IF 0.5 4区数学 Q3 MATHEMATICS

Geometriae Dedicata Pub Date : 2024-06-24 DOI:10.1007/s10711-024-00935-x

Stefano Marini, Nicoletta Tardini, Michela Zedda

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引用次数: 0

摘要

受Loi等人（Math Zeit 290:599-613，2018）中一个猜想的启发，我们证明了规则完整萨萨基流形上的凯勒锥是里奇平坦的，并且只有当它是平坦的时候，它才是投影诱导的。我们还得到，根据同调变换，同质紧凑萨萨基流形上的凯勒锥是投影诱导的。作为主要工具，我们提供了横向凯勒度量的凯勒势与锥形度量的凯勒势之间的关系。

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Projectively induced Kähler cones over regular Sasakian manifolds

Motivated by a conjecture in Loi et al. (Math Zeit 290:599–613, 2018) we prove that the Kähler cone over a regular complete Sasakian manifold is Ricci-flat and projectively induced if and only if it is flat. We also obtain that, up to \(\mathcal D_a\)—homothetic transformations, Kähler cones over homogeneous compact Sasakian manifolds are projectively induced. As main tool we provide a relation between the Kähler potentials of the transverse Kähler metric and of the cone metric.

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来源期刊

Geometriae Dedicata 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Geometriae Dedicata concentrates on geometry and its relationship to topology, group theory and the theory of dynamical systems. Geometriae Dedicata aims to be a vehicle for excellent publications in geometry and related areas. Features of the journal will include: A fast turn-around time for articles. Special issues centered on specific topics. All submitted papers should include some explanation of the context of the main results. Geometriae Dedicata was founded in 1972 on the initiative of Hans Freudenthal in Utrecht, the Netherlands, who viewed geometry as a method rather than as a field. The present Board of Editors tries to continue in this spirit. The steady growth of the journal since its foundation is witness to the validity of the founder''s vision and to the success of the Editors'' mission.