Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On projective manifolds with pseudo-effective tangent bundle   In this paper, we develop the theory of singular hermitian metrics on vector
bundles. As an application, we give a structure theorem of a projective
manifold $X$ with pseudo-effective tangent bundle: $X$ admits a smooth
fibration $X \to Y$ to a flat projective manifold $Y$ such that its general
fiber is rationally connected. Moreover, by applying this structure theorem, we
classify all the minimal surfaces with pseudo-effective tangent bundle and
study general non-minimal surfaces, which provide examples of (possibly
singular) positively curved tangent bundles.

31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph