| Summary: | The purpose of this paper is to investigate a warped product of hemi-slant submanifolds on an <i>S</i>-manifold. We prove many interesting results for the existence of warped product hemi-slant submanifold of the type <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>M</mi><mi>θ</mi></msub><msub><mo>×</mo><mi>f</mi></msub><msub><mi>M</mi><mo>⊥</mo></msub></mrow></semantics></math></inline-formula> with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ξ</mi><mi>α</mi></msub><mo>∈</mo><msub><mi>M</mi><mi>θ</mi></msub></mrow></semantics></math></inline-formula> of an <i>S</i>-manifold. For such submanifolds, a characterization theorem is proven. In addition, we form an inequality for the squared norm of the second fundamental form in terms of the warping function and the slant angle. We also provide some examples, and the equality case is also considered.
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