Andreas \v Cap, A. Rod Gover, Vladimir Sou\v cek
Conformally Invariant Operators via Curved Casimirs: Examples
The paper is published: Pure Appl. Math. Q. 6, 3 (2010) 693-714

MSC:

53A30 Conformal differential geometry

53A55 Differential invariants (local theory), geometric objects

58G35 Invariance and symmetry properties, See also {35A30}

53B15 Other connections

Abstract: We discuss a general scheme for a construction of linear conformally
invariant differential operators from curved Casimir operators; we
then explicitly carry this out for several examples. Apart from
demonstrating the efficacy of the approach via curved Casimirs, this
shows that this method applies both in regular and in singular
infinitesimal character, and also that it can be used to construct
standard as well as non--standard operators. The examples treated
include conformally invariant operators with leading term, in one
case, a square of the Laplacian, and in another case, a cube of the
Laplacian.


Keywords: conformally invariant operator, curved Casimir operator, power of the Laplacian
Notes: second and final version