We study the case of real homogeneous polynomial $P$ whose minimal real and complex decompositions in terms of powers of linear forms are different. In particularly we will show that, if the sum of the complex and the real ranks of $P$ is smaller or equal than $ 3deg(P)-1$, then the difference of the two decompositions is completely determined either on a line or on a conic.
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机译：我们研究实数齐次多项式$ P $的情况，其中最小实数和复数分解的线性形式幂不同。特别是，我们将表明，如果$ P $的复数和实际秩的总和小于或等于$ 3 deg（P）-1 $，则两个分解的差完全取决于a线或圆锥上。
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