Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariant pseudo-Sasakian and $K$-contact structures on
  seven-dimensional nilpotent Lie groups   We study the question of the existence of left-invariant Sasaki contact
structures on the seven-dimensional nilpotent Lie groups. It is shown that the
only Lie group allowing Sasaki structure with a positive definite metric tensor
is the Heisenberg group. We find a complete list of the 22 classes of
seven-dimensional nilpotent Lie groups which admit pseudo-Sasaki structure. We
also present a list of 25 classes of seven-dimensional nilpotent Lie groups
admitting a $K$-contact structure, but not the pseudo-Sasaki structure. All the
contact structures considered are central extensions of six-dimensional
nilpotent symplectic Lie groups and are established formulas that connect the
geometrical characteristics of the six-dimensional nilpotent almost
pseudo-K\"{a}hler Lie groups and seven-dimensional nilpotent contact Lie
groups. It is known that for the six-dimensional nilpotent pseudo-K\"{a}hler
Lie groups the Ricci tensor is always zero. Unlike the pseudo-K\"{a}hlerian
case, it is shown that on contact seven-dimensional algebras the Ricci tensor
is nonzero even in directions of the contact distribution.

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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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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
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess