253 research outputs found
Rarita-Schwinger Type Operators on Spheres and Real Projective Space
In this paper we deal with Rarita-Schwinger type operators on spheres and
real projective space. First we define the spherical Rarita-Schwinger type
operators and construct their fundamental solutions. Then we establish that the
projection operators appearing in the spherical Rarita-Schwinger type operators
and the spherical Rarita-Schwinger type equations are conformally invariant
under the Cayley transformation. Further, we obtain some basic integral
formulas related to the spherical Rarita-Schwinger type operators. Second, we
define the Rarita-Schwinger type operators on the real projective space and
construct their kernels and Cauchy integral formulas.Comment: 21 pages. arXiv admin note: text overlap with arXiv:1106.358
k-Dirac operator and parabolic geometries
The principal group of a Klein geometry has canonical left action on the
homogeneous space of the geometry and this action induces action on the spaces
of sections of vector bundles over the homogeneous space. This paper is about
construction of differential operators invariant with respect to the induced
action of the principal group of a particular type of parabolic geometry. These
operators form sequences which are related to the minimal resolutions of the
k-Dirac operators studied in Clifford analysis
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