CR流形到Kähler流形的半等距CR浸入及应用
Semi-isometric CR immersions of CR manifolds into Kähler manifolds and applications
摘要：
研究了从严格伪凸CR流形到Kähler流形的半等距CR浸入的第二基本型.作为应用，我们给出了实超曲面CR脐点的一个精确条件，推广了Webster关于一般实椭球上CR脐点不存在的一个著名定理.作为其他应用，我们将Ji-Yuan关于CR浸入球面的线性定理推广到三维流形的重要情形，并证明了Webster，Faran，Cima-Suffridge和Huang关于半等距CR浸入复欧几里得空间的"第一间隙“定理.我们的新方法的线性定理的基础上研究的第一个积极的特征值的Kohn-Laplacian。
英文摘要：
We study the second fundamental form of semi-isometric CR immersions from strictly pseudoconvex CR manifolds into Kähler manifolds. As an application, we give a precise condition for the CR umbilicality of real hypersurfaces, 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.
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