Huitao Feng's research while affiliated with Nankai University and other places
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Publications (7)
We first solve an open problem of S. Kobayashi in 1975 by proving that a holomorphic vector bundle on compact complex manifold is ample if and only if it admits a strongly pseudoconvex complex Finsler metric with positive Kobayashi curvature. We derive several applications which include: (1). the proof of the famous Lefschetz type theorem for gener...
In this paper, we solve a problem of Kobayashi posed in \cite{Ko4} by
introducing a Donaldson type functional on the space $F^+(E)$ of strongly
pseudo-convex complex Finsler metrics on $E$ -- a holomorphic vector bundle
over a closed K\"ahler manifold $M$. This Donaldson type functional is a
generalization in the complex Finsler geometry setting of...
In this short note, using Siu-Yau's method [14], we give a new proof that any n-dimensional compact Kähler manifold with positive orthogonal bisectional curvature must be biholomorphic to Pn.
In this paper, we introduce notions of nonlinear stabilities for a relative ample line bundle over a holomorphic fibration and define the notion of a geodesic-Einstein metric on this line bundle, which generalize the classical stabilities and Hermitian-Einstein metrics of holomorphic vector bundles. We introduce a Donaldson type functional to show...
In this paper, we present two kinds of total Chern forms $c(E,G)$ and
$\mathcal{C}(E,G)$ as well as a total Segre form $s(E,G)$ of a holomorphic
Finsler vector bundle $\pi:(E,G)\to M$ expressed by the Finsler metric $G$,
which answers a question of J. Faran (\cite{Faran}) to some extent. As some
applications, we show that the signed Segre forms $(-...
By using analytic method, we prove that there exist rational curves on
compact Hermitian manifolds with positive holomorphic bisectional curvature. It
confirms a question of S.-T. Yau. It is well-known that Mori proved in
\cite{Mori79} that every compact complex manifold $N$ with $c_1(N)>0$ contains
at least one rational curve. However, as a border...
Citations
... Other generalizations of Theorem 1.1 include generalizations to compact Hermitian manifolds ([Buc99; LY87]), and very recent work of Feng-Liu-Wan [FLW18], which expanded Theorem 1.1 to include the existence of Finsler-Einstein metrics. ...
... There are many other characterizations of projective spaces for which we refer to [3,4,8,18,19,27,28,36,45,51,55] and the references therein. ...
... It is easy to check that the above definition is equivalent to the Definition 3.1 in T. Aikou [4]. There are also other notions of complex Finsler-Einstein vector bundle, we refer to [17] and some recent progress in [11,12] along this line. ...
... It is easy to check that the above definition is equivalent to the Definition 3.1 in T. Aikou [4]. There are also other notions of complex Finsler-Einstein vector bundle, we refer to [17] and some recent progress in [11,12] along this line. ...
