quaternionic heisenberg group
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2019 ◽  
Vol 19 (3) ◽  
pp. 415-420
Author(s):  
Moritz Gruber

Abstract The filling volume functions of the n-th quaternionic Heisenberg group grow, up to dimension n, as fast as the ones of the Euclidean space. We identify the growth rate of the filling volume function in dimension n + 1, which is strictly faster than the growth rate of the (n + 1)-dimensional filling volume function of the Euclidean space.


2017 ◽  
Vol 2019 (18) ◽  
pp. 5649-5673
Author(s):  
Stefan Ivanov ◽  
Ivan Minchev ◽  
Dimiter Vassilev

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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