Holomorphic functions and regular quaternionic functions on the hyperkähler space H
| dc.creator | Perotti, Alessandro | |
| dc.date | 2007-11-28 | |
| dc.date.accessioned | 2026-07-07T08:45:47Z | |
| dc.date.available | 2026-07-07T08:45:47Z | |
| dc.description | Let H be the space of quaternions, with its standard hypercomplex structure. Let R(D) be the module of regular functions on D. For every unitary vector p in S^2, R(D) contains the space of holomorphic functions w.r.t. the complex structure J_p induced by p. We prove the existence, on any bounded domain D, of regular functions that are not J_p-holomorphic for any p. Our starting point is a result of Chen and Li concerning maps between hyperkaehler manifolds, where a similar result is obtained for a less restricted class of quaternionic maps. We give a criterion, based on the energy-minimizing property of holomorphic maps, that distinguishes J_p-holomorphic functions among regular functions. | |
| dc.description | Proceedings V ISAAC Congress Catania 2005 (to appear) | |
| dc.identifier | https://arxiv.org/abs/0711.4440 | |
| dc.identifier | http://arxiv.org/abs/0711.4440 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143074 | |
| dc.subject | Complex Variables | |
| dc.subject | 32A30; 53C26; 30G35 | |
| dc.title | Holomorphic functions and regular quaternionic functions on the hyperkähler space H | |
| dc.type | text |