The intersection of two real forms in Hermitian symmetric spaces of compact type. (English) Zbl 1260.53107

Suh, Young Jin (ed.) et al., Proceedings of the 16th international workshop on differential geometry and the 5th KNUGRG-OCAMI differential geometry workshop, Taegu, Korea, October 31–November 3, 2012. Taegu: National Institute for Mathematical Sciences and Grassmann Research Group. 89-96 (2012).
Summary: This talk is based on my joint work with Hiroyuki Tasaki. A real form in a Hermitian symmetric space \(M\) of compact type is the fixed point set of an involutive anti-holomorphic isometry of \(M\), which is connected and a totally geodesic Lagrangian submanifold. We prove that the intersection of two real forms is an antipodal set in which the geodesic symmetry at each point is the identity. Using this, we investigate the intersection of two real forms in irreducible \(M\) as well as non-irreducible \(M\) and determine the intersection numbers of them.
For the entire collection see [Zbl 1254.53004].


53C40 Global submanifolds
53D12 Lagrangian submanifolds; Maslov index