INDEX adjoint representation of a Lie algebra, 58 adjoint space of a symmetric space, 48 Bianchi identity first, 3, 8 second, 8 Blaschke problem, ix, xiii branching law, 98, 176, 223, 235 Calabi sequence, 20 Cartan decomposition, 26, 59, 87, 118, 137, 266 Cartan's lemma, 283 Cartan subalgebra, 57, 59, 67, 98, 109, 170, 271, 341 Casimir element, 58­60, 177, 223 Cayley algebra, 89, 113 Cayley plane, 88, 112­113 infinitesimal rigidity of, 113 curvature of, 94 functions on, 96­98 infinitesimal rigidity of, 107­112 as a Hermitian symmetric space, 87 local K¨ hler geometry of, 99 a spectrum of, 97 Ricci tensor of, 94 complex quadric, 27, 134­243, 339­340 closed geodesic of, 199 curvature of, 139 differential forms of degree one on, 237­243, of dimension four, 157­159, 182, 172­173, 234­237, 283 of dimension three, 223­229 of dimension two, 190­192 functions on, 177­180 as a Hermitian symmetric space, 138 infinitesimal rigidity of, 229, 232­234 local K¨ hler geometry of, 146­152 a