STATIONARY CURVATURES OF TWO-DIMENSIONAL TOTALLY GEODESIC SUBMANIFOLDS IN THE GRASSMANNIAN OF BIVECTORS

摘要

An infinitesimal criterion indicating when a two-dimensional submanifold of a Riemannian symmetric space is totally geodesic is given. As an application, the classification of two-dimensional totally geodesic submanifolds of the Grassmannian of bivectors is given in a new way, and it is proved that the sectional curvature takes stationary values on tangent spaces of such submanifolds.