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

Gasqui, Jacques; Goldschmidt, Hubert

J. Reine Angew. Math. 396, 87-121 (1989).

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

Keywords:

symmetric space; zero-energy condition; closed geodesics; complex projective spaces; complex quadrics; infinitesimally rigid