On polynomial integrability of the Euler equations on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi mathvariant="fraktur">s</mml:mi><mml:mi mathvariant="fraktur">o</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>4</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>
Journal of geometry and physics