Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Holomorphic Euler number of K$\ddot{a}$hler manifolds with almost
  nonnegative Ricci curvature   Let $M^n$ be a compact K$\ddot{a}$hler manifold with almost nonnegative Ricci
curvature and nonzero first Betti number. We show that the holomorphic Euler
number of $M^n$ vanishes, which gives a new obstruction for compact complex
manifolds admitting K$\ddot{a}$hler metrics with almost nonnegative Ricci
curvature. A crucial step in the proof is to show a vanishing theorem of
Dolbeault-Morse-Novikov cohomology.

21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat