| Summary: | In this paper, we give some classifications of the <i>k</i>-Yamabe solitons on the hypersurfaces of the Euclidean spaces from the vector field point of view. In several results on <i>k</i>-Yamabe solitons with a concurrent vector field on submanifolds in Riemannian manifolds, is proved that a <i>k</i>-Yamabe soliton <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><msup><mi>M</mi><mi>n</mi></msup><mo>,</mo><mi>g</mi><mo>,</mo><msup><mi>v</mi><mi>T</mi></msup><mo>,</mo><mi>λ</mi><mo>)</mo></mrow></semantics></math></inline-formula> on a hypersurface in the Euclidean space <inline-formula><math display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></semantics></math></inline-formula> is contained either in a hypersphere or a hyperplane. We provide an example to support this study and all of the results in this paper can be implemented to Yamabe solitons for <i>k</i>-curvature with <inline-formula><math display="inline"><semantics><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>.
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