The purpose of the present paper is to give an elementary method for the computation of the cohomology groups Hq（X,Ω^p X（L））, （0 ≤q ≤ n） of an n-dimensional non-primary Hopf manifold X with arbitrary fundamen...The purpose of the present paper is to give an elementary method for the computation of the cohomology groups Hq（X,Ω^p X（L））, （0 ≤q ≤ n） of an n-dimensional non-primary Hopf manifold X with arbitrary fundamental group. We use the method of Zhou to generalize the results for primary Hopf manifolds and non-primary Hopf manifold with an Abelian fundamental group.展开更多
Let X be a Hopf manifolds with an Abelian fundamental group.E is a holomorphic vector bundle of rank r with trivial pull-back to W=■~n-{0}.We prove the existence of a non-vanishing section of L■E for some line bundl...Let X be a Hopf manifolds with an Abelian fundamental group.E is a holomorphic vector bundle of rank r with trivial pull-back to W=■~n-{0}.We prove the existence of a non-vanishing section of L■E for some line bundle on X and study the vector bundles filtration structure of E. These generalize the results of D.Mall about structure theorem of such a vector bundle E.展开更多
In the present note that grew out of my talk given at the conference in honor of Prof. Zhong Tongde,I give a survey of some recent results about holomorphic vector bundles over general Hopf manifolds.
We discuss the properties of complex manifolds having rational homology of S 1 × S 2n?1 including those constructed by Hopf, Kodaira and Brieskorn-van de Ven. We extend certain previously known properties of coho...We discuss the properties of complex manifolds having rational homology of S 1 × S 2n?1 including those constructed by Hopf, Kodaira and Brieskorn-van de Ven. We extend certain previously known properties of cohomology of bundles on such manifolds. As an application we consider degeneration of Hodge-de Rham spectral sequence in this non Kahler setting.展开更多
Let X be a Hopf manifold with non-Abelian fundamental group and E be a holomorphic vector bundle over X,with trivial pull-back to C^n-{0}.The authors show that there exists a line bundle L over X such that E■L has a ...Let X be a Hopf manifold with non-Abelian fundamental group and E be a holomorphic vector bundle over X,with trivial pull-back to C^n-{0}.The authors show that there exists a line bundle L over X such that E■L has a nowhere vanishing section.It is proved that in case dim(X)≥3,π*(E)is trivial if and only if E is filtrable by vector bundles.With the structure theorem,the authors get the cohomology dimension of holomorphic bundle E over X with trivial pull-back and the vanishing of Chern class of E.展开更多
We give a complete classification of holomorphic endomorphisms of Hopf manifolds in dimensions two and three.In particular,we show that these endomorphisms are automorphisms except for the diagonal class,in which case...We give a complete classification of holomorphic endomorphisms of Hopf manifolds in dimensions two and three.In particular,we show that these endomorphisms are automorphisms except for the diagonal class,in which case they are quasi-homogeneous.展开更多
In this paper, we use a kind of main part symmetry scheme to study the center manifolds and Hop f bifurcations for ODEs, and set up a kind of method for calculation them.
基金supported by 973 Project Foundation of China and Outstanding Youth science Grant of NSFC(Grant No.19825105)
文摘The purpose of the present paper is to give an elementary method for the computation of the cohomology groups Hq（X,Ω^p X（L））, （0 ≤q ≤ n） of an n-dimensional non-primary Hopf manifold X with arbitrary fundamental group. We use the method of Zhou to generalize the results for primary Hopf manifolds and non-primary Hopf manifold with an Abelian fundamental group.
基金The research was supported by 973 Project Foundation of China and the Outstanding Youth Science Grant of NSFC(grant no.19825105)
文摘Let X be a Hopf manifolds with an Abelian fundamental group.E is a holomorphic vector bundle of rank r with trivial pull-back to W=■~n-{0}.We prove the existence of a non-vanishing section of L■E for some line bundle on X and study the vector bundles filtration structure of E. These generalize the results of D.Mall about structure theorem of such a vector bundle E.
基金supported by National Science Foundation of China(Grant Nos.10421101,10721061
文摘In the present note that grew out of my talk given at the conference in honor of Prof. Zhong Tongde,I give a survey of some recent results about holomorphic vector bundles over general Hopf manifolds.
文摘We discuss the properties of complex manifolds having rational homology of S 1 × S 2n?1 including those constructed by Hopf, Kodaira and Brieskorn-van de Ven. We extend certain previously known properties of cohomology of bundles on such manifolds. As an application we consider degeneration of Hodge-de Rham spectral sequence in this non Kahler setting.
基金supported by the National Natural Science Foundation of China(Nos.11671330,11688101,11431013).
文摘Let X be a Hopf manifold with non-Abelian fundamental group and E be a holomorphic vector bundle over X,with trivial pull-back to C^n-{0}.The authors show that there exists a line bundle L over X such that E■L has a nowhere vanishing section.It is proved that in case dim(X)≥3,π*(E)is trivial if and only if E is filtrable by vector bundles.With the structure theorem,the authors get the cohomology dimension of holomorphic bundle E over X with trivial pull-back and the vanishing of Chern class of E.
基金supported by National Natural Science Foundation of China(Grant No.11871333).
文摘We give a complete classification of holomorphic endomorphisms of Hopf manifolds in dimensions two and three.In particular,we show that these endomorphisms are automorphisms except for the diagonal class,in which case they are quasi-homogeneous.
文摘In this paper, we use a kind of main part symmetry scheme to study the center manifolds and Hop f bifurcations for ODEs, and set up a kind of method for calculation them.
