Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalizing axioms of $r$-planes and $r$-spheres on Riemannian and
  K\"ahler manifolds   The famous theorems of Cartan, related to the axiom of $r$-planes, and
Leung-Nomizu about the axiom of $r$-spheres were extended to K\"ahler geometry
by several authors.
  In this paper we replace the strong notions of totally geodesic submanifolds
($r$-planes) and extrinsic spheres ($r$-spheres) by a wider class of special
isometric immersions such that theorems of type "axioms of $r$-special
submanifolds" could hold. We verify also that there are plenty of special
submanifolds in real and complex space forms and, in the codimension one case,
in Einstein manifolds.

21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol