The Reflection Map and Infinitesimal Deformations of Sphere Mappings

The reflection map introduced by D’Angelo is applied to deduce simpler descriptions of nondegeneracy conditions for sphere maps and to the study of infinitesimal deformations of sphere maps. It is shown that the dimension of the space of infinitesimal deformations of a nondegenerate sphere map is bo...

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Detalles Bibliográficos
Autor principal: Reiter, Michael
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2019
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7819958/
https://www.ncbi.nlm.nih.gov/pubmed/33519167
http://dx.doi.org/10.1007/s12220-019-00298-w
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author Reiter, Michael
author_facet Reiter, Michael
author_sort Reiter, Michael
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description The reflection map introduced by D’Angelo is applied to deduce simpler descriptions of nondegeneracy conditions for sphere maps and to the study of infinitesimal deformations of sphere maps. It is shown that the dimension of the space of infinitesimal deformations of a nondegenerate sphere map is bounded from above by the explicitly computed dimension of the space of infinitesimal deformations of the homogeneous sphere map. Moreover a characterization of the homogeneous sphere map in terms of infinitesimal deformations is provided.
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spelling pubmed-78199582021-01-28 The Reflection Map and Infinitesimal Deformations of Sphere Mappings Reiter, Michael J Geom Anal Article The reflection map introduced by D’Angelo is applied to deduce simpler descriptions of nondegeneracy conditions for sphere maps and to the study of infinitesimal deformations of sphere maps. It is shown that the dimension of the space of infinitesimal deformations of a nondegenerate sphere map is bounded from above by the explicitly computed dimension of the space of infinitesimal deformations of the homogeneous sphere map. Moreover a characterization of the homogeneous sphere map in terms of infinitesimal deformations is provided. Springer US 2019-10-29 2021 /pmc/articles/PMC7819958/ /pubmed/33519167 http://dx.doi.org/10.1007/s12220-019-00298-w Text en © The Author(s) 2019 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Reiter, Michael
The Reflection Map and Infinitesimal Deformations of Sphere Mappings
title The Reflection Map and Infinitesimal Deformations of Sphere Mappings
title_full The Reflection Map and Infinitesimal Deformations of Sphere Mappings
title_fullStr The Reflection Map and Infinitesimal Deformations of Sphere Mappings
title_full_unstemmed The Reflection Map and Infinitesimal Deformations of Sphere Mappings
title_short The Reflection Map and Infinitesimal Deformations of Sphere Mappings
title_sort reflection map and infinitesimal deformations of sphere mappings
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7819958/
https://www.ncbi.nlm.nih.gov/pubmed/33519167
http://dx.doi.org/10.1007/s12220-019-00298-w
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