On Penrose integral formula and series expansion of k-regular functions on the quaternionic space Hn☆

  title={On Penrose integral formula and series expansion of k-regular functions on the quaternionic space Hn☆},
  author={Qianqian Kang and Wei Wang},
  journal={Journal of Geometry and Physics},

The tangential k-Cauchy–Fueter complexes and Hartogs’ phenomenon over the right quaternionic Heisenberg group

  • Yun ShiWei Wang
  • Mathematics
    Annali di Matematica Pura ed Applicata (1923 -)
  • 2019
We construct the tangential $k$-Cauchy-Fueter complexes on the right quaternionic Heisenberg group, as the quaternionic counterpart of $\overline{\partial}_b$-complex on the Heisenberg group in the

A Version of Schwarz Lemma Associated to the k-Cauchy–Fueter Operator

The k-Cauchy–Fueter operator is an Euclidean version of the helicity k/2 massless field equations on affine Minkowski space. In this article, a version of Schwarz lemma associated to the

On twistor transformations and invariant differential operator of simple Lie group G2(2)

The twistor transformations associated to the simple Lie group G2 are described explicitly. We consider the double fibration G2/P2←ηG2/B→τG2/P1, where P1 and P2 are two parabolic subgroups of G2 and

On the tangential Cauchy-Fueter operators on nondegenerate quadratic hypersurfaces in H 2

On quadratic hypersurfaces in H 2 , we find the explicit forms of tangential Cauchy-Fueter operators and associated tangential Laplacians (cid:2) b . Then by using the Fourier transformation on the

On quaternionic complexes over unimodular quaternionic manifolds

  • Wei Wang
  • Mathematics
    Differential Geometry and its Applications
  • 2018

The Neumann Problem for the k-Cauchy–Fueter Complex over k-Pseudoconvex Domains in $$\mathbb {R}^4$$R4 and the $$L^2$$L2 Estimate

The k-Cauchy–Fueter operator and complex are quaternionic counterparts of the Cauchy–Riemann operator and the Dolbeault complex in the theory of several complex variables, respectively. To develop

A variational approach to the quaternionic Monge–Ampère equation

In this paper, we use the variational method to solve the quaternionic Monge–Ampère equation when the right-hand side is a positive measure of finite energy. We introduce finite energy classes of



Regular functions of several quaternionic variables and the Cauchy-Fueter complex

We employ a classical idea of Ehrenpreis, together with a new algebraic result, to give a new proof that regular functions of several quaternionic variables cannot have compact singularities. As a

Hartog's Phenomenon For Polyregular Functions And Projective Dimension Of Related Modules Over A Pol

In this paper we prove that the projective dimension of Mn = R 4 =hAni is 2n ? 1, where R is the ring of polynomials in 4n variables with complex coeecients, and hAni is the module generated by the

Cohomology and massless fields

The geometry of twistors was first introduced in Penrose [28]. Since that time it has played a significant role in solutions of various problems in mathemetical physics of both a linear and nonlinear

Analysis of the module determining the properties of regular functions of several quaternionic variables

For a polynomial ring, R,in 4 n variables over a field,we consider the submodule of R 4 corresponding to the 4 × 4n matrix made up of n groupings of the linear representation of quarternions with

Penrose transformation and complex integral geometry

A survey is given of results on the representation of solutions of systems of massless equations in terms of solutions of the Cauchy-Riemann equations on the space of Penrose twisters. A detailed