Let M be a complete Kähler surface andbe a symplectic surface which is smoothly immersed in M.Letαbe the Kähler angle ofin M.In the previous paper Han and Li(JEMS 12:505–527,2010)2010,we study the symple...Let M be a complete Kähler surface andbe a symplectic surface which is smoothly immersed in M.Letαbe the Kähler angle ofin M.In the previous paper Han and Li(JEMS 12:505–527,2010)2010,we study the symplectic critical surfaces,which are critical points of the functional L=1 cosαdμin the class of symplectic surfaces.In this paper,we calculate the second variation of the functional L and derive some consequences.In particular,we show that,if the scalar curvature of M is positive,is a stable symplectic critical surface with cosα≥δ>0,whose normal bundle admits a holomorphic section X∈L2(),thenis holomorphic.We construct symplectic critical surfaces in C2.We also prove a Liouville theorem for symplectic critical surfaces in C2.展开更多
基金The research was supported the National Natural Science Foundation of China,No.11131007,No.11471014The research was also supported by the Doctoral Programme Foundation of Institution of Higher Education of China,No.20110002110064.
文摘Let M be a complete Kähler surface andbe a symplectic surface which is smoothly immersed in M.Letαbe the Kähler angle ofin M.In the previous paper Han and Li(JEMS 12:505–527,2010)2010,we study the symplectic critical surfaces,which are critical points of the functional L=1 cosαdμin the class of symplectic surfaces.In this paper,we calculate the second variation of the functional L and derive some consequences.In particular,we show that,if the scalar curvature of M is positive,is a stable symplectic critical surface with cosα≥δ>0,whose normal bundle admits a holomorphic section X∈L2(),thenis holomorphic.We construct symplectic critical surfaces in C2.We also prove a Liouville theorem for symplectic critical surfaces in C2.
