Mathematics – Complex Variables
Scientific paper
2007-11-28
Mathematics
Complex Variables
Proceedings V ISAAC Congress Catania 2005 (to appear)
Scientific paper
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.
No associations
LandOfFree
Holomorphic functions and regular quaternionic functions on the hyperkähler space H does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Holomorphic functions and regular quaternionic functions on the hyperkähler space H, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Holomorphic functions and regular quaternionic functions on the hyperkähler space H will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-249043