By means of the theory of harmonic maps into the unitary group U(N), the authors study harmonic maps into the symplectic group Sp(N). The symplectic uniton and symplectic ex--tended uniton are introduced. The method o...By means of the theory of harmonic maps into the unitary group U(N), the authors study harmonic maps into the symplectic group Sp(N). The symplectic uniton and symplectic ex--tended uniton are introduced. The method of the symplectic Backlund transformation and the Darboux transformation is used to construct new symplectic unitons from a known one.展开更多
The authors give an algebraic method to add uniton numbers for harmonic maps from a simply connected domain ? ? R2∪{∞} into the unitary group U(N) with ?nite uniton number. So, it is proved that any n-uniton can be ...The authors give an algebraic method to add uniton numbers for harmonic maps from a simply connected domain ? ? R2∪{∞} into the unitary group U(N) with ?nite uniton number. So, it is proved that any n-uniton can be obtained from a 0-uniton by purely algebraic operations and integral transforms to solve the ?ˉ-problem via two different ways.展开更多
Further geometry and topology for pseudo-holomorphic curves in complex Grassmannians Gm(CN) are studied. Some curvature pinching theorems for pseudo- holomorphic curyes with constant Kahler angles in Gm(CN) are obtain...Further geometry and topology for pseudo-holomorphic curves in complex Grassmannians Gm(CN) are studied. Some curvature pinching theorems for pseudo- holomorphic curyes with constant Kahler angles in Gm(CN) are obtained, so that the corresponding results for pseudoholomorphic curves in complex projective spaces are generalized.展开更多
The Ribaucour transformations for flat Lagrangian submanifolds in Cn and CPn via loop group actions are given. As a consequence, the authors obtain a family of new flat Lagrangian submanifolds from a given one via a p...The Ribaucour transformations for flat Lagrangian submanifolds in Cn and CPn via loop group actions are given. As a consequence, the authors obtain a family of new flat Lagrangian submanifolds from a given one via a purely algebraic algorithm. At the same time, it is shown that such Ribaucour transformation always comes with a permutability formula.展开更多
基金Project supported by the National Natural Science Foundation of China (No.19531050)the Scientific Foundation of the Minnstr
文摘By means of the theory of harmonic maps into the unitary group U(N), the authors study harmonic maps into the symplectic group Sp(N). The symplectic uniton and symplectic ex--tended uniton are introduced. The method of the symplectic Backlund transformation and the Darboux transformation is used to construct new symplectic unitons from a known one.
基金Project supported by the National Natural Science Foundation of China (No.12071106) and the Science Foundation of the Ministry of Education of China.
文摘The authors give an algebraic method to add uniton numbers for harmonic maps from a simply connected domain ? ? R2∪{∞} into the unitary group U(N) with ?nite uniton number. So, it is proved that any n-uniton can be obtained from a 0-uniton by purely algebraic operations and integral transforms to solve the ?ˉ-problem via two different ways.
文摘Further geometry and topology for pseudo-holomorphic curves in complex Grassmannians Gm(CN) are studied. Some curvature pinching theorems for pseudo- holomorphic curyes with constant Kahler angles in Gm(CN) are obtained, so that the corresponding results for pseudoholomorphic curves in complex projective spaces are generalized.
基金Project supported by the National Natural Science Foundation of China (No.10271106)the Education Commission of Zhejiang Province of China (No.20030342).
文摘The Ribaucour transformations for flat Lagrangian submanifolds in Cn and CPn via loop group actions are given. As a consequence, the authors obtain a family of new flat Lagrangian submanifolds from a given one via a purely algebraic algorithm. At the same time, it is shown that such Ribaucour transformation always comes with a permutability formula.
