## Rigidité infinitésimale des espaces projectifs et des quadriques complexes. (Infinitesimal rigidity of projective spaces and complex quadrics).(French)Zbl 0657.53029

Let X be a compact symmetric space. A symmetric 2-form h on X satisfies the zero-energy condition if the integrals of h along closed geodesics all vanish. We say that X is infinitesimally rigid if the only symmetric 3-forms on X satisfying the zero-energy condition are the Lie derivatives of the metric. We prove that the complex projective spaces of dimension $$\geq 2$$ and the complex quadrics of dimension $$\geq 5$$ are infinitesimally rigid.
Reviewer: J.Gasqui

### MSC:

 53C35 Differential geometry of symmetric spaces
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