Nonlinear Liouville theorem in the quaternionic Heisenberg group

2005 ◽  
Vol 10 (2) ◽  
pp. 355-357
Author(s):  
Yang Qiao-hua ◽  
Zhu Fu-liu
Keyword(s):  
Heisenberg Group ◽  
Liouville Theorem ◽  
Quaternionic Heisenberg Group

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

scholarly journals Quaternionic Heisenberg Group and Heterotic String Solutions with Non-Constant Dilaton in Dimensions 7 and 5

2015 ◽  
Vol 339 (1) ◽  
pp. 199-219 ◽  
Author(s):  
Marisa Fernández ◽  
Stefan Ivanov ◽  
Luis Ugarte ◽  
Dimiter Vassilev
Keyword(s):  
Heisenberg Group ◽  
Heterotic String ◽  
Quaternionic Heisenberg Group ◽  
Constant Dilaton

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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