Geometry of reflective submanifolds in Riemannian symmetric spaces

Abstract

The set $\mathscr{R}$(B) of submanifolds conjugate to a given reflective submanifold B in a Riemannian symmetric space M has a structure of symmetric space. Using this structure, for a submanifold N in M we establish integral formulae which represent the integrals of the functions C $\mapsto$ vol(N∩C) on $\mathscr{R}$(B) by some extrinsic geometric amounts of N.