Page 14 - Curvature and Homology

xiv NOTATION INDEX

symbor page
D(M). D(M) : d-cohomology ring. p-dimensional d-co-
8
homology group ......... 15

bp : pth betti number .......... 60. 63
......
bq.r : complex dimension of Ay 177
d: differential operator ......... 14. 168
df. #f : differential operator of type (1.0). (0. 1) . 168. 233
a: boundary operator ......... 21.58. 61
*. *-I : star operator. inverse of star oberator . 66. 70. 97
6: co-differential operator ....... 72. 170. 233
: co-differential operator of type (- 1.0).
(0.- 1) ............. 170
A : Laplace-Beltrami operator ...... 73. 233
H: Harmonic projector ......... 80. 178
G: Green's operator .......... 80. I78
g,*. Q)* : induced maps of g, ......... 18
A:. A:= A:. .................. 15. 74
A;. A%: .................. 74
D, : covariant differential operator .... 24
Dx : covariant differential operator .... 192
Q : Ricci operator ........... 87
€(I) : exterior product by operator .... 96
i(X) : interior product by X operator .... 97. 171
@(x) Lie derivative operator ....... 101. 134
:
J: almost complex structure tensor ... 151
V $ VoJ : space of vectors of bidegree (1.0). (0. 1) . 152
~ q : ~ r space of exterior forms of bidegree (q. r) 152
r\$ : space of harmonic forms of bidegree (q. r) 177
52: fundamental 2-form ......... 165
L = e(Q) : .................. 170
A=(-l)P*L*: .................. 170

O(n) = O(n. R) : The subgroup of GL(n. R) consisting of those
matrices a for .which 'a = a-l where a-1 is the inverse of a and
.
ta denotes its transpose : '(a:) = (4) -
U(n) = {a E GL(n. C) I d = La--1). where d = (a:) .
SU(n) = {a E U(n) det (a) = 1) .
1