| Summary: | The aim of this paper is to construct a sharp general inequality for warped product pseudo-slant submanifold of the type <inline-formula> <math display="inline"> <semantics> <mrow> <mi>M</mi> <mo>=</mo> <msub> <mi>M</mi> <mo>⊥</mo> </msub> <msub> <mo>×</mo> <mi>f</mi> </msub> <msub> <mi>M</mi> <mi>θ</mi> </msub> </mrow> </semantics> </math> </inline-formula>, in a nearly cosymplectic manifold, in terms of the warping function and the symmetric bilinear form <i>h</i> which is known as the second fundamental form. The equality cases are also discussed. As its application, we establish a bound for the first non-zero eigenvalue of the warping function whose base manifold is compact.
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