Abstract This paper defines chain and $\mathbf{R}$-circle on quaternionic hyperbolic space, and gives the property of chains under the vertical projection. The uniqueness of chain passing through two distinct points and qc-horizontality of $\mathbf{R}$-circles are proved, and the relationship between $\mathbf{R}$-circle and pure imaginary $\mathbf{R}$-circle is given.
SHI Yun. Chain and $\mathbf{R}$-circle on quaternionic Heisenberg group and their properties. Applied Mathematics A Journal of Chinese Universities, 2016, 31(1): 90-100.
