Semi-isometric CR immersions of CR manifolds into Kähler manifolds and applications

• Duong Ngoc Son ^[1]
  1. [1] University of Vienna

     University of Vienna

     Innere Stadt, Austria

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 22, Nº 2, 2021, págs. 957-987
• Idioma: inglés
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• Resumen

  • We study the second fundamental form of semi-isometric CR immer- sions from strictly pseudoconvex CR manifolds into K ̈ahler manifolds. As an application, we give a precise condition for the CR umbilicality of real hyper- surfaces, extending an well-known theorem by Webster on the nonexistence of CR umbilical points on generic real ellipsoids. As other applications, we extend the linearity theorem of Ji-Yuan for CR immersions into spheres with vanishing second fundamental form to the important case of three-dimensional manifolds, and prove the “first gap” theorem in the spirit of Webster, Faran, Cima-Suffridge, and Huang for semi-isometric CR immersions into a complex Euclidean space of “low” codimension. Our new approach to the linearity theorem is based on the study of the first positive eigenvalue of the Kohn Laplacian