Journal of Symplectic Geometry

Volume 13 (2015)

Number 4

Deforming symplectomorphism of certain irreducible Hermitian symmetric spaces of compact type by mean curvature flow

Pages: 905 – 962

DOI: http://dx.doi.org/10.4310/JSG.2015.v13.n4.a4

Authors

Guangcun Lu (School of Mathematical Sciences, Beijing Normal University, and Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, China)

Bang Xiao (School of Mathematical Sciences, Beijing Normal University, and Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, China)

Abstract

In this paper, we generalize Medos–Wang’s arguments and results on the mean curvature ow deformations of symplectomorphisms of $\mathbb{C}P^n$ in [MeWa] to complex Grassmann manifold $G(n, n + m; \mathbb{C})$ and compact totally geodesic Kähler–Einstein submanifolds of it. We also give an abstract result and discuss the case of complex tori.

Full Text (PDF format)