In this note, we prove that the symplectic blow-up or blow-down in the dimension 4 is rigid, i.e. the symplectic area of the divisor does not exceed the symplectic radius of the neighbourhood on which we do the blow-u...In this note, we prove that the symplectic blow-up or blow-down in the dimension 4 is rigid, i.e. the symplectic area of the divisor does not exceed the symplectic radius of the neighbourhood on which we do the blow-up or blow-down.展开更多
The self-duality concept for the Higgs field is handled in the presence of contact geometry in 5 dimensions. A non-trivial SO（3） Higgs field lives only on the fifth dimension of the contact manifold because of the c...The self-duality concept for the Higgs field is handled in the presence of contact geometry in 5 dimensions. A non-trivial SO（3） Higgs field lives only on the fifth dimension of the contact manifold because of the contact structure, while the SD Yang-Mills field lives in the 4-dimensional hyperplane of the contact manifold. The Higgs and SD Yang-Mills fields do not interact with one another.展开更多
基金Supported in part by the NSF of P. R. China the Foundation of Chinese Educational Committee for Returned Scholars.
文摘In this note, we prove that the symplectic blow-up or blow-down in the dimension 4 is rigid, i.e. the symplectic area of the divisor does not exceed the symplectic radius of the neighbourhood on which we do the blow-up or blow-down.
文摘The self-duality concept for the Higgs field is handled in the presence of contact geometry in 5 dimensions. A non-trivial SO（3） Higgs field lives only on the fifth dimension of the contact manifold because of the contact structure, while the SD Yang-Mills field lives in the 4-dimensional hyperplane of the contact manifold. The Higgs and SD Yang-Mills fields do not interact with one another.
基金Supported by the Science Foundation of China University of PetroleumBeijing(2462015YQ0604)partially by the Personnel Training and Academic Development Fund(2462015QZDX02)
