<p>In this paper, we classify the centroaffine hypersurfaces whose difference tensor <i>K</i> satisfies the conditions <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(K_{T}X=\alpha X,\ X(\alpha )=0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>K</mi> <mi>T</mi> </msub> <mi>X</mi> <mo>=</mo> <mi>α</mi> <mi>X</mi> <mo>,</mo> <mspace width="4pt" /> <mi>X</mi> <mrow> <mo stretchy="false">(</mo> <mi>α</mi> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> for any <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(X\perp T, ~X\in \mathfrak {X}(M)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>X</mi> <mo>⊥</mo> <mi>T</mi> <mo>,</mo> <mspace width="3.33333pt" /> <mi>X</mi> <mo>∈</mo> <mi mathvariant="fraktur">X</mi> <mo stretchy="false">(</mo> <mi>M</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> with a differentiable function <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> together with studying their relations with affine hyperspheres. Under certain conditions, we show that such centroaffine hypersurfaces equipped with the centroaffine metric are the warped product of an interval and the affine hyperspheres. Moreover, we give the explicit expressions for such centroaffine hypersurfaces.</p>