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Zbl 0739.53042
Gasqui, Jacques
Infinitesimal rigidity and geometry of the complex quadric of dimension 4. (Rigidité infinitésimale et géométrie de la quadrique complexe de dimension 4.) (French)
[J] Sémin. Théor. Spectrale Géom., Chambéry-Grenoble 9, Année 1990-1991, 141-152 (1991).

A symmetric 2-form on a compact symmetric Riemannian space $(X,g)$ satisfies the zero-energy condition if all its integrals along the closed geodesics of $X$ vanish. The space $(X,g)$ is infinitesimally rigid if the only symmetric 2-forms on $X$ satisfying the zero-energy condition are the Lie derivatives of the metric $g$. In the work of the author and {\it H. Goldschmidt} [J. Reine Angew. Math. 396, 87-121 (1989; Zbl 0657.53029)], the authors have studied the infinitesimal rigidity of the complex quadric $Q\sb n$ in $P\sb{n+1}(C)$ for $n\ge 5$. When $n=4$ the used method breaks down. So, in this work, one presents a new method, for the study of the infinitesimal rigidity of $Q\sb 4$, inspired in part by {\it R. Michel's} work [Bull. Soc. Math. Fr. 101, 17-69 (1973; Zbl 0265.53041)] and based on a good preparation concerning the Kählerian geometry of this quadric.
[V.Cruceanu (Iaşi)]

MSC 2000:: *53C35 Symmetric spaces (differential geometry)
53C55 Complex differential geometry (global)

Keywords: Hermitian symmetric space; oriented real structure; Lichnerowicz Laplacian; infinitesimal rigidity; complex quadric

Citations: Zbl 0657.53029; Zbl 0265.53041

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	Scientific prize winners of the ICM 2010
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	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

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