The hypoelliptic Laplacian on X = G/K 41 2.14 The scaling of the form B For t > 0, we denote with an extra subscript t the above operators associated with the form B/t. By (2.12.19), it is clear that · · ( T XN ) i /2 X -N ( T XN ) /2 t N D b,t t = t D g,X + c Y N , Y T X t N 1 TX 1 TX i + tD + E - i tD + E N . (2.14.1) b t t For a > 0, set K a s (x, Y ) = s (x, aY ) . (2.14.2) By (2.14.1), we get · · ( T XN ) /2 X -N ( T XN ) /2 D b,t t (2.14.3) K t t N K -1 = tD X tb . t By (2.13.4), (2.14.3), we obtain K t t N · ( T XN ) /2 L X t -N b,t · ( T XN ) /2 -1 K t = tL X tb . (2.14.4) 2.15 The Bianchi identity The classical Bianchi identity says that