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

نویسندگان

چکیده

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

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ژورنال

عنوان ژورنال: Annali della Scuola normale superiore di Pisa. Classe di scienze

سال: 2021

ISSN: ['0391-173X', '2036-2145']

DOI: https://doi.org/10.2422/2036-2145.201902_008