非紧型黎曼对称空间间的调和黎曼淹没

IF 0.8 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2024-09-25 DOI:10.1112/blms.13155

F. E. Burstall

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引用次数: 0

摘要

我们构造了谐波黎曼淹没，它们是从对称非紧型空间缩回到它们的秩一全测地线子空间。在这些结果中，我们证明了与分裂实数半单李群相关的黎曼对称空间中的一个非常数的、全局定义的复值调和态射的存在性。这完成了对Gudmundsson猜想的肯定证明。

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Harmonic Riemannian submersions between Riemannian symmetric spaces of noncompact type

We construct harmonic Riemannian submersions that are retractions from symmetric spaces of noncompact type onto their rank-one totally geodesic subspaces. Among the consequences, we prove the existence of a nonconstant, globally defined complex-valued harmonic morphism from the Riemannian symmetric space associated to a split real semisimple Lie group. This completes an affirmative proof of a conjecture of Gudmundsson.

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