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 $C \mapsto \mathrm{vol}(N \cap C)$
on $\mathscr{R}(B)$
by some extrinsic geometric amounts of $N$ .
@article{1145287102,
author = {TASAKI, Hiroyuki},
title = {Geometry of reflective submanifolds in Riemannian symmetric spaces},
journal = {J. Math. Soc. Japan},
volume = {58},
number = {3},
year = {2006},
pages = { 275-297},
language = {en},
url = {http://dml.mathdoc.fr/item/1145287102}
}
TASAKI, Hiroyuki. Geometry of reflective submanifolds in Riemannian symmetric spaces. J. Math. Soc. Japan, Tome 58 (2006) no. 3, pp. 275-297. http://gdmltest.u-ga.fr/item/1145287102/