Wensheng Cao
Jorgensen's Inequalities and Collars in n-dimensional Quaternionic Hyperbolic Space.
Tue, 01/26/2010 - 16:01 — SomNambulAuthors: Wensheng Cao, John R. Parker
Subjects: Geometric Topology
AbstractIn this paper, we obtain analogues of Jorgensen's inequality for
non-elementary groups of isometries of quaternionic hyperbolic $n$-space
generated by two elements, one of which is loxodromic. Our result gives some
improvement over earlier results of Kim [10] and Markham [15]}. These results
also apply to complex hyperbolic space and give improvements on results of
Jiang, Kamiya and Parker [7]Algebraic Characterization of the Isometries of the Complex and Quaternionic Hyperbolic Plane.
Tue, 09/08/2009 - 12:16 — SomNambulAuthors: Wensheng Cao, Krishnendu Gongopadhyay
Subjects: Geometric Topology
AbstractLet $\F$ denote either of $\R$, $\C$ or the quaternions $\H$. Let $H^2_{\F}$
denote the two dimensional hyperbolic space over $\F$. The algebraic
characterization of the isometries of $H^2_{\R}$ and $H^3_{\R}$ in terms of
their trace and determinant are foundational in the real hyperbolic geometry.
The counterpart of this characterization for isometries of $H^2_{\C}$ was given
by Giraud and Goldman. In this paper we offer algebraic characterization for
the isometries of $H^2_{\H}$.Algebraic Characterization of the Isometries of the Complex and Quaternionic Hyperbolic Plane.
Tue, 09/08/2009 - 12:16 — SomNambulAuthors: Wensheng Cao, Krishnendu Gongopadhyay
Subjects: Geometric Topology
AbstractLet $\F$ denote either of $\R$, $\C$ or the quaternions $\H$. Let $H^2_{\F}$
denote the two dimensional hyperbolic space over $\F$. The algebraic
characterization of the isometries of $H^2_{\R}$ and $H^3_{\R}$ in terms of
their trace and determinant are foundational in the real hyperbolic geometry.
The counterpart of this characterization for isometries of $H^2_{\C}$ was given
by Giraud and Goldman. In this paper we offer algebraic characterization for
the isometries of $H^2_{\H}$.
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