ON THE LAGRANGIAN ANGLE AND THE K?HLER ANGLE OF IMMERSED SURFACES IN THE COMPLEX PLANE C^ 2  

作　　者：Xingxiao LI Xiao LI 李兴校;李晓(School of Mathematics and Information Sciences,Henan Normal University,Xinxiang 453007,China;School of Mathematics and Statistics,Southwest University,Chongqing 400715,China)

机构地区：[1]School of Mathematics and Information Sciences,Henan Normal University,Xinxiang 453007,China [2]School of Mathematics and Statistics,Southwest University,Chongqing 400715,China

出　　处：《Acta Mathematica Scientia》2019年第6期1695-1712,共18页数学物理学报（B辑英文版）

基　　金：supported by National Natural Science Foundation of China(11671121,11871197)

摘　　要：In this paper, we discuss the Lagrangian angle and the K?hler angle of immersed surfaces in C2. Firstly, we provide an extension of Lagrangian angle, Maslov form and Maslov class to more general surfaces in C2 than Lagrangian surfaces, and then naturally extend a theorem by J.-M. Morvan to surfaces of constant K?hler angle, together with an application showing that the Maslov class of a compact self-shrinker surface with constant K?hler angle is generally non-vanishing. Secondly, we obtain two pinching results for the K?hler angle which imply rigidity theorems of self-shrinkers with K?hler angle under the condition that ∫M|h|2e-|x|2/2 dVM< ∞, where h and x denote, respectively, the second fundamental form and the position vector of the surface.In this paper,we discuss the Lagrangian angle and the Kahler angle of immersed surfaces in C^2.Firstly,we provide an extension of Lagrangian angle,Maslov form and Maslov class to more general surfaces in C^2 than Lagrangian surfaces,and then naturally extend a theorem by J.-M.Morvan to surfaces of constant Kahler angle,together with an application showing that the Maslov class of a compact self-shrinker surface with constant Kahler angle is generally non-vanishing.Secondly,we obtain two pinching results for the Kahler angle which imply rigidity theorems of self-shrinkers with Kahler angle under the condition that∫M|h|^2e^-|x|^2/2dVM<∞,where h and x denote,respectively,the second fundamental form and the position vector of the surface.

关 键 词：KAHLER ANGLE LAGRANGIAN ANGLE self-shrinker 

分 类 号：O17[理学—数学]