Studies are made of the cohomology of CR_ submanifolds and integrability of the distribution D of CR_submanifolds. When dim D⊥】1, the totally umbilical non-trival CR-submanifold i n nea r Kaehler manifold is totall...Studies are made of the cohomology of CR_ submanifolds and integrability of the distribution D of CR_submanifolds. When dim D⊥】1, the totally umbilical non-trival CR-submanifold i n nea r Kaehler manifold is totally geodesic. In the end, we get:If is n ear Kaehler manifold with B】0, then is not permitt ed to have fixed foliate non-trival CR-submanifold.展开更多
In this paper, we investigate the Dirichlet problem for Hermitian-Einstein equation on complex vector bundle over almost Hermitian manifold, and we obtain the unique solution of the Dirichlet problem for Hermitian-Ein...In this paper, we investigate the Dirichlet problem for Hermitian-Einstein equation on complex vector bundle over almost Hermitian manifold, and we obtain the unique solution of the Dirichlet problem for Hermitian-Einstein equation.展开更多
Recently, Tedi Draghici and Weiyi Zhang studied Donaldson＇s ＂tamed to compatible＂ question （Draghici T, Zhang W. A note on exact forms on almost complex manifolds, arXiv： 1111. 7287vl [math. SC]. Submitted on 30 ...Recently, Tedi Draghici and Weiyi Zhang studied Donaldson＇s ＂tamed to compatible＂ question （Draghici T, Zhang W. A note on exact forms on almost complex manifolds, arXiv： 1111. 7287vl [math. SC]. Submitted on 30 Nov. 2011）. That is, for a compact almost complex 4-manifold whose almost complex structure is tamed by a symplectic form, is there a symplectic form compatible with this almost complex structure？ They got several equivalent forms of this problem by studying the space of exact forms on such a manifold. With these equivalent forms, they proved a result which can be thought as a further partial answer to Donaldson＇s question in dimension 4. In this note, we give another simpler proof of their result.展开更多
1. Let S<sup>4</sup> be a four-sphere and let G<sub>2</sub>（TS<sup>4</sup>） be the Grassmann bundle on S<sup>4</sup> with natural Riemann metric and almost complex str...1. Let S<sup>4</sup> be a four-sphere and let G<sub>2</sub>（TS<sup>4</sup>） be the Grassmann bundle on S<sup>4</sup> with natural Riemann metric and almost complex structure. G<sub>2</sub>（TS<sup>4</sup>） is called （1, 2）-symplectic if the （1, 2）part of dk is zero where k is the K（?）hler form of G<sub>2</sub>（TS<sup>4</sup>）. In this note, we prove the following theorem:展开更多
Let σ be an anti-holomorphic involution on an almost complex four manifold X,a necessary and sufficient condition is given to determine weather X/σ admits an almost complex structure.
文摘Studies are made of the cohomology of CR_ submanifolds and integrability of the distribution D of CR_submanifolds. When dim D⊥】1, the totally umbilical non-trival CR-submanifold i n nea r Kaehler manifold is totally geodesic. In the end, we get:If is n ear Kaehler manifold with B】0, then is not permitt ed to have fixed foliate non-trival CR-submanifold.
基金supported in part by National Natural Science Foundation of China (Grant No. 10901147)supported in part by National Natural Science Foundation of China (Grant Nos. 10831008 and 11071212)the Ministry of Education Doctoral Fund 20060335133
文摘In this paper, we investigate the Dirichlet problem for Hermitian-Einstein equation on complex vector bundle over almost Hermitian manifold, and we obtain the unique solution of the Dirichlet problem for Hermitian-Einstein equation.
基金The NSF(11071208 and 11126046)of Chinathe Postgraduate Innovation Project(CXZZ13 0888)of Jiangsu Province
文摘Recently, Tedi Draghici and Weiyi Zhang studied Donaldson＇s ＂tamed to compatible＂ question （Draghici T, Zhang W. A note on exact forms on almost complex manifolds, arXiv： 1111. 7287vl [math. SC]. Submitted on 30 Nov. 2011）. That is, for a compact almost complex 4-manifold whose almost complex structure is tamed by a symplectic form, is there a symplectic form compatible with this almost complex structure？ They got several equivalent forms of this problem by studying the space of exact forms on such a manifold. With these equivalent forms, they proved a result which can be thought as a further partial answer to Donaldson＇s question in dimension 4. In this note, we give another simpler proof of their result.
文摘1. Let S<sup>4</sup> be a four-sphere and let G<sub>2</sub>（TS<sup>4</sup>） be the Grassmann bundle on S<sup>4</sup> with natural Riemann metric and almost complex structure. G<sub>2</sub>（TS<sup>4</sup>） is called （1, 2）-symplectic if the （1, 2）part of dk is zero where k is the K（?）hler form of G<sub>2</sub>（TS<sup>4</sup>）. In this note, we prove the following theorem:
基金supported by the National Natural Science Foundation of China(Grant No.10371008).
文摘Let σ be an anti-holomorphic involution on an almost complex four manifold X,a necessary and sufficient condition is given to determine weather X/σ admits an almost complex structure.
