The conformal curvature tensor
Cλμνω of a Riemann space
Vn,
n≥6, admitting a group of motions of order
r>
n(
n+1)/2-(3
n-11) is studied with the use of tensor calculus. The form of
Cλμνω is obtained by virtue of the fact that the equations
XCλμνω=0 can contain at most a certain number of linearly independent equations. The
Cλμνω is in general of the form
Cλμνω=
C[δ
λωδ
μν-δ
λνδ
μω] -((n-1)/2)
C[δ
λω(A
μA
ν+B
μB
ν)+δ
μν (A
λA
ω+B
λB
ω)-δ
λν (A
μA
ω+B
μB
ω)-δ
μω(A
λA
ν+B
λB
ν)]+((n-1) (n-2)/2)
C [A
λA
ωB
μB
ν+A
μA
νB
λB
ω -A
λA
νB
μB
ω-A
μA
ωB
λB
ν]
with A
αA
α=B
αB
α=1, A
αB
α=0. But for
n=6, 8 some other form is also possible.
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