کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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1896645 | 1044443 | 2011 | 18 صفحه PDF | دانلود رایگان |
The Cauchy–Fueter operator on the quaternionic space HnHn induces the tangential Cauchy–Fueter operator on the boundary of a domain. The quaternionic Heisenberg group is a standard model of the boundaries. By using the Penrose transformation associated to a double fibration of homogeneous spaces of Sp(2N,C), we construct an exact sequence on the quaternionic Heisenberg group, the tangential kk-Cauchy–Fueter complex, resolving the tangential kk-Cauchy–Fueter operator Q0(k). Q0(1) is the tangential Cauchy–Fueter operator. The complex gives the compatible conditions under which the non-homogeneous tangential kk-Cauchy–Fueter equations Q0(k)u=f are solvable. The operators in this complex are left invariant differential operators on the quaternionic Heisenberg group. This is a quaternionic version of ∂¯b-complex on the Heisenberg group in the theory of several complex variables.
Journal: Journal of Geometry and Physics - Volume 61, Issue 1, January 2011, Pages 363–380