Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sasakian metric as a Ricci soliton and related results   We prove the following results: (i) A Sasakian metric as a non-trivial Ricci
soliton is null $\eta$-Einstein, and expanding. Such a characterization permits
to identify the Sasakian metric on the Heisenberg group $\mathcal{H}^{2n+1}$ as
an explicit example of (non-trivial) Ricci soliton of such type. (ii) If an
$\eta$-Einstein contact metric manifold $M$ has a vector field $V$ leaving the
structure tensor and the scalar curvature invariant, then either $V$ is an
infinitesimal automorphism, or $M$ is $D$-homothetically fixed $K$-contact.

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The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc