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A general optimal inequality for warped product submanifolds in paracosymplectic manifolds. (English) Zbl 1388.53021

Summary: The aim of this paper is to study the pseudo-Riemannian warped product submanifolds of a paracosymplectic manifold \(\bar{M}\). We first, prove some fundamental lemmas and then derive some important results with parallel canonical structures on \(\mathcal{PR}\)-semi-invariant submanifolds \(M\) of \(\bar{M}\). Finally, we describe the warped product submanifold \(M\) of \(\bar{M}\) by developing the general optimal inequality in terms of warping function and squared norm of second fundamental form. We also consider the totally geodesic, mixed geodesic and equality case of the inequality.

MSC:

53B25 Local submanifolds
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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