# Rigidity of CR morphisms between compact strongly pseudoconvex CR manifolds

Journal of the European Mathematical Society (2011)

- Volume: 013, Issue: 1, page 175-184
- ISSN: 1435-9855

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topYau, Stephen S.-T.. "Rigidity of CR morphisms between compact strongly pseudoconvex CR manifolds." Journal of the European Mathematical Society 013.1 (2011): 175-184. <http://eudml.org/doc/277470>.

@article{Yau2011,

abstract = {Let $X_1$ and $X_2$ be two compact strongly pseudoconvex CR manifolds of dimension $2n-1\ge 5$ which bound complex varieties $V_1$ and $V_2$ with only isolated normal singularities in $\mathbb \{C\}^\{N1\}$ and $\mathbb \{C\}^\{N2\}$ respectively. Let $S_1$ and $S_2$ be the singular sets of $V_1$ and $V_2$ respectively and $S_2$ is nonempty. If $2n-N_2-1\ge 1$ and the cardinality of $S_1$ is less than 2 times the cardinality of $S_2$, then we prove that any non-constant CR morphism from $X_1$ to $X_2$ 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.},

author = {Yau, Stephen S.-T.},

journal = {Journal of the European Mathematical Society},

keywords = {strongly pseudoconvex CR manifold; rigidity of CR morphism; geometric genus of compact embeddable CR manifold; strongly pseudoconvex CR manifold; rigidity of CR morphism; geometric genus of compact embeddable CR manifold},

language = {eng},

number = {1},

pages = {175-184},

publisher = {European Mathematical Society Publishing House},

title = {Rigidity of CR morphisms between compact strongly pseudoconvex CR manifolds},

url = {http://eudml.org/doc/277470},

volume = {013},

year = {2011},

}

TY - JOUR

AU - Yau, Stephen S.-T.

TI - Rigidity of CR morphisms between compact strongly pseudoconvex CR manifolds

JO - Journal of the European Mathematical Society

PY - 2011

PB - European Mathematical Society Publishing House

VL - 013

IS - 1

SP - 175

EP - 184

AB - Let $X_1$ and $X_2$ be two compact strongly pseudoconvex CR manifolds of dimension $2n-1\ge 5$ which bound complex varieties $V_1$ and $V_2$ with only isolated normal singularities in $\mathbb {C}^{N1}$ and $\mathbb {C}^{N2}$ respectively. Let $S_1$ and $S_2$ be the singular sets of $V_1$ and $V_2$ respectively and $S_2$ is nonempty. If $2n-N_2-1\ge 1$ and the cardinality of $S_1$ is less than 2 times the cardinality of $S_2$, then we prove that any non-constant CR morphism from $X_1$ to $X_2$ 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.

LA - eng

KW - strongly pseudoconvex CR manifold; rigidity of CR morphism; geometric genus of compact embeddable CR manifold; strongly pseudoconvex CR manifold; rigidity of CR morphism; geometric genus of compact embeddable CR manifold

UR - http://eudml.org/doc/277470

ER -

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