Let X be a non-primary Hopf Surface with Abelian fundamental group π1 （X）（≌） Z Zm, L a line bundle on X, we give a formula for computing the dimension of cohomology H^q（X,Ω^P（L）） and the explicit results fo...Let X be a non-primary Hopf Surface with Abelian fundamental group π1 （X）（≌） Z Zm, L a line bundle on X, we give a formula for computing the dimension of cohomology H^q（X,Ω^P（L）） and the explicit results for non-primary exceptional Hopf surface.展开更多
The existence of the Hopf bifurcation of a complex ordinary differential equation system in the complex domain is studied in this paper by using the complex qualitative theory.In the complex domain,we conclude that th...The existence of the Hopf bifurcation of a complex ordinary differential equation system in the complex domain is studied in this paper by using the complex qualitative theory.In the complex domain,we conclude that the Hopf bifurcation appears for both directions of the parameter μ. The formulae of the Hopf bifurcation are also given in this paper.展开更多
Under broad hypotheses we derive a scalar reduction of the generalized Kähler-Ricci soliton system.We realize solutions as critical points of a functional,analogous to the classical Aubin energy,defined on an orb...Under broad hypotheses we derive a scalar reduction of the generalized Kähler-Ricci soliton system.We realize solutions as critical points of a functional,analogous to the classical Aubin energy,defined on an orbit of the natural Hamiltonian action of diffeomorphisms,thought of as a generalized Kähler class.This functional is convex on a large set of paths in this space,and using this we show rigidity of solitons in their generalized Kähler class.As an application we prove uniqueness of the generalized Kähler-Ricci solitons on Hopf surfaces constructed in Streets and Ustinovskiy[Commun.Pure Appl.Math.74(9),1896-1914(2020)],finishing the classification in complex dimension 2.展开更多
基金Supported by NNSF(10171068)Supported by Beijing Excellent Talent Grant(20042D0500509)
文摘Let X be a non-primary Hopf Surface with Abelian fundamental group π1 （X）（≌） Z Zm, L a line bundle on X, we give a formula for computing the dimension of cohomology H^q（X,Ω^P（L）） and the explicit results for non-primary exceptional Hopf surface.
文摘The existence of the Hopf bifurcation of a complex ordinary differential equation system in the complex domain is studied in this paper by using the complex qualitative theory.In the complex domain,we conclude that the Hopf bifurcation appears for both directions of the parameter μ. The formulae of the Hopf bifurcation are also given in this paper.
基金V.A.was supported in part by an NSERC Discovery Grant and a Connect Talent Grant of the Région Pays de la Loire.
文摘Under broad hypotheses we derive a scalar reduction of the generalized Kähler-Ricci soliton system.We realize solutions as critical points of a functional,analogous to the classical Aubin energy,defined on an orbit of the natural Hamiltonian action of diffeomorphisms,thought of as a generalized Kähler class.This functional is convex on a large set of paths in this space,and using this we show rigidity of solitons in their generalized Kähler class.As an application we prove uniqueness of the generalized Kähler-Ricci solitons on Hopf surfaces constructed in Streets and Ustinovskiy[Commun.Pure Appl.Math.74(9),1896-1914(2020)],finishing the classification in complex dimension 2.
