Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral estimates and discreteness of spectra under Riemannian
  submersions   For Riemannian submersions, we establish some estimates for the spectrum of
the total space in terms of the spectrum of the base space and the geometry of
the fibers. In particular, for Riemannian submersions of complete manifolds
with closed fibers of bounded mean curvature, we show that the spectrum of the
base space is discrete if and only if the spectrum of the total space is
discrete.

33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph