In this paper we completely classify the homogeneous two-spheres,especially,the minimal homogeneous ones in the quaternionic projective space HPn.According to our classification,more minimal constant curved two-sphere...In this paper we completely classify the homogeneous two-spheres,especially,the minimal homogeneous ones in the quaternionic projective space HPn.According to our classification,more minimal constant curved two-spheres in HPnare obtained than what Ohnita conjectured in the paper"Homogeneous harmonic maps into complex projective spaces.Tokyo J Math,1990,13:87–116".展开更多
This note studies the Chern-Simons invariant of a closed oriented Riemannian 3-manifold M. The first achievement is to establish the formula CS（e） - CS（e） = degA, where e and e are two （global） frames of M, and...This note studies the Chern-Simons invariant of a closed oriented Riemannian 3-manifold M. The first achievement is to establish the formula CS（e） - CS（e） = degA, where e and e are two （global） frames of M, and A ： M → SO（3） is the ＂difference＂ map. An interesting phenomenon is that the ＂jumps＂ of the Chern-Simons integrals for various frames of many 3-manifolds are at least two, instead of one. The second purpose is to give an explicit representation of CS（e＋） and CS（e_）, where e＋ and e_ are the ＂left＂ and ＂right＂ quaternionic frames on M3 induced from an immersion M^3 → E^4, respectively. Consequently we find many metrics on S^3 （Berger spheres） so that they can not be conformally embedded in E^4.展开更多
The Bott generator of the homotopy group π2k-1U（∞） is used to construct an almost complex structure on S^6, which is integrable except a small neighborhood.
In this paper, the authors present a method to construct the minimal and H-minimal Lagrangian submanifolds in complex hyperquadric Q_n from submanifolds with special properties in odd-dimensional spheres. The authors ...In this paper, the authors present a method to construct the minimal and H-minimal Lagrangian submanifolds in complex hyperquadric Q_n from submanifolds with special properties in odd-dimensional spheres. The authors also provide some detailed examples.展开更多
We first prove a basic theorem with respect to the moving frame along a Lagrangian immersion into the complex projective space CPn. Applying this theorem, we study the rigidity problem of Lagrangian submanifolds in CPn.
基金supported by National Natural Science Foundation of China(Grant Nos.11471299,11401481 and 11331002)。
文摘In this paper we completely classify the homogeneous two-spheres,especially,the minimal homogeneous ones in the quaternionic projective space HPn.According to our classification,more minimal constant curved two-spheres in HPnare obtained than what Ohnita conjectured in the paper"Homogeneous harmonic maps into complex projective spaces.Tokyo J Math,1990,13:87–116".
基金Supported by NSFC (Grant Nos. 10531090 and 10229101)Chang Jiang Scholars Program
文摘This note studies the Chern-Simons invariant of a closed oriented Riemannian 3-manifold M. The first achievement is to establish the formula CS（e） - CS（e） = degA, where e and e are two （global） frames of M, and A ： M → SO（3） is the ＂difference＂ map. An interesting phenomenon is that the ＂jumps＂ of the Chern-Simons integrals for various frames of many 3-manifolds are at least two, instead of one. The second purpose is to give an explicit representation of CS（e＋） and CS（e_）, where e＋ and e_ are the ＂left＂ and ＂right＂ quaternionic frames on M3 induced from an immersion M^3 → E^4, respectively. Consequently we find many metrics on S^3 （Berger spheres） so that they can not be conformally embedded in E^4.
基金Project supported by the Changjiang Scholars Programthe Outstanding Youth Foundation of China (No. 19925103, No. 10229101)the National Natural Science Foundation of China (No. 10531090).
文摘The Bott generator of the homotopy group π2k-1U（∞） is used to construct an almost complex structure on S^6, which is integrable except a small neighborhood.
基金supported by the National Natural Science Foundation of China(Nos.11331002,11471299,11871445)。
文摘In this paper, the authors present a method to construct the minimal and H-minimal Lagrangian submanifolds in complex hyperquadric Q_n from submanifolds with special properties in odd-dimensional spheres. The authors also provide some detailed examples.
文摘We first prove a basic theorem with respect to the moving frame along a Lagrangian immersion into the complex projective space CPn. Applying this theorem, we study the rigidity problem of Lagrangian submanifolds in CPn.
