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

2019 ◽  
Vol 199 (2) ◽  
pp. 651-680 ◽  
Author(s):  
Yun Shi ◽  
Wei Wang
Keyword(s):  
Heisenberg Group ◽  
Hartogs Phenomenon ◽  
The Right ◽  
Quaternionic Heisenberg Group

Semilinear PDEs in the Heisenberg group: The role of the right invariant vector fields

2010 ◽  
Vol 72 (2) ◽  
pp. 987-997 ◽  
Author(s):  
Isabeau Birindelli ◽  
Fausto Ferrari ◽  
Enrico Valdinoci
Keyword(s):  
Heisenberg Group ◽  
Vector Fields ◽  
Invariant Vector ◽  
Semilinear Pdes ◽  
The Right ◽  
Invariant Vector Fields

scholarly journals CONJUGATE POINTS ON THE QUATERNIONIC HEISENBERG GROUP

2003 ◽  
Vol 40 (1) ◽  
pp. 61-72 ◽  
Author(s):  
Chang-Rim Jang ◽  
Jun-Kon Kim ◽  
Yeon-Wook Kim ◽  
Keun Park
Keyword(s):  
Heisenberg Group ◽  
Conjugate Points ◽  
Quaternionic Heisenberg Group

Existence for singular critical exponential (𝑝, 𝑄) equations in the Heisenberg group

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Patrizia Pucci ◽  
Letizia Temperini
Keyword(s):  
Heisenberg Group ◽  
Elliptic Operator ◽  
Exponential Growth ◽  
Singular Behavior ◽  
Nontrivial Solutions ◽  
Right Hand ◽  
Critical Exponential Growth ◽  
The Right

Abstract The paper deals with the existence of nontrivial solutions for ( p , Q ) (p,Q) equations in the Heisenberg group H n \mathbb{H}^{n} with critical exponential growth at infinity and a singular behavior at the origin. The main features and novelty of the paper are the above generality on the right-hand side of the equation, the ( p , Q ) (p,Q) growth of the elliptic operator and the fact that the equation is studied in the entire Heisenberg group.

scholarly journals Non-Umbilical Quaternionic Contact Hypersurfaces in Hyper-Kähler Manifolds

2017 ◽  
Vol 2019 (18) ◽  
pp. 5649-5673
Author(s):  
Stefan Ivanov ◽  
Ivan Minchev ◽  
Dimiter Vassilev
Keyword(s):  
Heisenberg Group ◽  
Kähler Manifold ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Totally Umbilical ◽  
Kahler Manifold ◽  
Compact Case ◽  
Quaternionic Heisenberg Group

Abstract It is shown that any compact quaternionic contact (qc) hypersurfaces in a hyper-Kähler manifold which is not totally umbilical has an induced qc structure, locally qc homothetic to the standard 3-Sasakian sphere. In the non-compact case, it is proved that a seven-dimensional everywhere non-umbilical qc-hypersurface embedded in a hyper-Kähler manifold is qc-conformal to a qc-Einstein structure which is locally qc-equivalent to the 3-Sasakian sphere, the quaternionic Heisenberg group or the hyperboloid.

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