# On the Hodge-type decomposition and cohomology groups of k-Cauchy–Fueter complexes over domains in the quaternionic space

@article{Chang2016OnTH, title={On the Hodge-type decomposition and cohomology groups of k-Cauchy–Fueter complexes over domains in the quaternionic space}, author={Der-Chen Chang and Irina Markina and Wei Wang}, journal={Journal of Geometry and Physics}, year={2016}, volume={107}, pages={15-34} }

## 6 Citations

On the weighted L2 estimate for the k-Cauchy–Fueter operator and the weighted k-Bergman kernel

- Mathematics
- 2017

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

- Mathematics
- 2019

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…

On quaternionic complexes over unimodular quaternionic manifolds

- MathematicsDifferential Geometry and its Applications
- 2018

The resolution of Euclidean massless field operators of higher spins on $\Bbb R^6$ and the $L^2$ method

- Mathematics
- 2021

The resolution of 4-dimensional massless field operators of higher spins was constructed by Eastwood-Penrose-Wells by using the twistor method. Recently physicists are interested in 6dimensional…

Sub-Riemannian Geometry and Hypoelliptic Operators

- Mathematics
- 2017

In this course we carefully define the notion of a non-holonomic manifold, which is a manifold with a certain non-integrable smooth sub-bundle of the tangent bundle, also called a distribution. We…

The Resolution of Euclidean Massless Field Operators of Higher Spins on
$${\mathbb {R}}^6$$
R
6

- MathematicsComplex Analysis and Operator Theory
- 2022

The resolution of 4 dimensional massless field operators of higher spins was constructed by Eastwood–Penrose–Wells by using the twistor method. Recently physicists are interested in 6 dimensional…

## References

SHOWING 1-10 OF 30 REFERENCES

The k-Cauchy–Fueter complex, Penrose transformation and Hartogs phenomenon for quaternionic k-regular functions

- Mathematics
- 2010

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

- Mathematics
- 2013

Complexes of invariant operators in several quaternionic variables

- Mathematics
- 2006

Much attention has recently been paid to a study of analogues of the Dolbeault complex for the Dirac equation in several vector variables. In this article, we study these questions in dimension 4, in…

On non-homogeneous Cauchy–Fueter equations and Hartogs’ phenomenon in several quaternionic variables

- Mathematics
- 2008

Cohomology and massless fields

- Mathematics
- 1981

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…

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

- Mathematics
- 1999

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…

On the Cauchy–Szegö Kernel for Quaternion Siegel Upper Half-Space

- Mathematics
- 2013

The work is dedicated to the construction of the Cauchy–Szegö kernel for the Cauchy–Szegö projection integral operator from the space of $$L^2$$-integrable functions defined on the boundary of the…