It is known that there is a 1-1 correspondence between the first cohomology of the sheaf O(-k-2) over the projective space and the solutions to the k-Cauchy-Fueter equations on the quaternionic space Hn.We find an exp...It is known that there is a 1-1 correspondence between the first cohomology of the sheaf O(-k-2) over the projective space and the solutions to the k-Cauchy-Fueter equations on the quaternionic space Hn.We find an explicit Radon-Penrose type integral formula to realize this correspondence:given a -closed(0,1)form f with coefficients in the(-k-2)th power of the hyperplane section bundle H-k-2,there is an integral representation Pf such that ι*(Pf) is a solution to the k-Cauchy-Fueter equations,where ι is an embedding of the quaternionic space Hn into C4n.展开更多
基金supported by National Natural Science Foundation of China (Grant No.11171298)
文摘It is known that there is a 1-1 correspondence between the first cohomology of the sheaf O(-k-2) over the projective space and the solutions to the k-Cauchy-Fueter equations on the quaternionic space Hn.We find an explicit Radon-Penrose type integral formula to realize this correspondence:given a -closed(0,1)form f with coefficients in the(-k-2)th power of the hyperplane section bundle H-k-2,there is an integral representation Pf such that ι*(Pf) is a solution to the k-Cauchy-Fueter equations,where ι is an embedding of the quaternionic space Hn into C4n.
