Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Quasi-Einstein Manifolds in Contact Geometry   In this study, we investigate generalized quasi-Einstein structure for normal
metric contact pair manifolds. Firstly, we deal with elementary properties and
examine, existence, and characterizations of generalized quasi-Einstein normal
metric contact pair manifold. Secondly, the generalized quasi-constant
curvature of normal metric contact pair manifolds are studied and it is proven
that a normal metric contact pair manifold with generalized quasi-constant
curvature is a generalized quasi-Einstein manifold. Normal metric contact pair
manifolds satisfying cyclic Ricci tensor and the Codazzi type of Ricci tensor
are considered and its shown that a generalized quasi-Einstein normal metric
contact pair manifold does not satisfy Codazzi type of Ricci tensor. Finally,
we work on normal metric contact pair manifolds satisfying certain curvature
conditions related to $ \mathcal{M}- $projective, conformal, and concircular
curvature tensors. We show that a normal metric contact pair manifold with
generalized quasi-constant curvature is locally isometric to the Hopf manifold
$ S^{2n+1}(1) \times S^1 $.

23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con