Geodesic
Rigidity of CR morphisms between compact strongly pseudoconvex CR manifolds
Journal of the European Mathematical Society, Tome 13 (2011) no. 1, pp. 175-184

Voir la notice de l'article provenant de la source EMS Press

Let X1​ and X2​ be two compact strongly pseudoconvex CR manifolds of dimension 2n−1≥5 which bound complex varieties V1​ and V2​ with only isolated normal singularities in CN1​ and CN2​ respectively. Let S1​ and S2​ be the singular sets of V1​ and V2​ respectively and S2​ is nonempty. If 2n–N2​–1≥1 and the cardinality of S1​ is less than 2 times the cardinality of S2​, then we prove that any non-constant CR morphism from X1​ to X2​ is necessarily a CR biholomorphism. On the other hand, let X be a compact strongly pseudoconvex CR manifold of dimension 3 which bounds a complex variety V with only isolated normal non-quotient singularities. Assume that the singular set of V is nonempty. Then we prove that any non-constant CR morphism from X to X is necessarily a CR biholomorphism.
DOI : 10.4171/jems/247
Classification : 32-XX, 14-XX, 00-XX
Keywords: Strongly pseudoconvex CR manifold, rigidity of CR morphism, geometric genus of compact embeddable CR manifold 
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     title = {Rigidity of {CR} morphisms between compact strongly pseudoconvex {CR} manifolds},
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Stephen S.-T. Yau. Rigidity of CR morphisms between compact strongly pseudoconvex CR manifolds. Journal of the European Mathematical Society, Tome 13 (2011) no. 1, pp. 175-184. doi: 10.4171/jems/247

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