Edited in collaboration with the Grassmann Research Group, this book contains many important articles delivered at the ICM 2014 Satellite Conference and the 18th International Workshop on Real and Complex Submanifolds, which was held at the National Institute for Mathematical Sciences, Daejeon, Republic of Korea, August 1012, 2014.

The book covers various aspects of differential geometry focused on submanifolds, symmetric spaces, Riemannian and Lorentzian manifolds, and Kähler and Grassmann manifolds.

Provides classification problems and some new results in real and complex Grassmann manifolds Introduces recent progress in geometric structures developed on Lagrangian submanifolds, Riemannian symmetric spaces, and Lorentzian manifolds Presents investigations of several kinds of geometric properties on Riemannian manifolds by famous differential geometers from all over the world