The Tangential $$\varvec{k}$$-Cauchy–Fueter Operator and $$\varvec{k}$$-CF Functions Over the Heisenberg Group

Ren, Guangzhen; Shi, Yun; Wang, Wei

doi:10.1007/s00006-020-1043-3

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2020

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Cited by 9 publications

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“…The construction of this paper is based on the fact that V 0 and V 1 in (6) span an abelian subalgebra. Its real version plays a very important role in developing a theory of quaternionic Monge-Ampère operator in [14] and tangential k-Cauchy-Fueter complex [12] over the Heisenberg group.…”

Section: Introductionmentioning

confidence: 99%

Anti-self-dual connections over the $5$D Heisenberg group and the twistor method

Ren¹,

Wang²

2021

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In this paper, we introduce notions of α-planes in 5D complex Heisenberg group and the twistor space as the moduli space of all α-planes. So we can define an anti-self-dual (ASD) connection as a connection flat over all α-planes. This geometric approach allows us to establish Penrose-Ward correspondence between ASD connections over 5D complex Heisenberg group and a class of holomorphic vector bundles on the twistor space. By Atiyah-Ward ansätz, we also construct a family of ASD connections on 5D complex Heisenberg group. When restricted to 5D real Heisenberg group, the flat model of 5D contact manifolds, an ASD connection satisfies the horizontal part of the contact instanton equation introduced by physicists.

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Section: Introductionmentioning

confidence: 99%