Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the existence of balanced and SKT metrics on nilmanifolds   On a complex manifold an Hermitian metric which is simultaneously SKT and
balanced has to be necessarily K\"ahler. It has been conjectured that if a
compact complex manifold (M,J) has an SKT metric and a balanced metric both
compatible with J, then (M, J) is necessarily K\"ahler. We show that the
conjecture is true for nilmanifolds.

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The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin