Abstract
In this paper we obtain the cosine hyperbolic and sine hyperbolic rules for a dual hyperbolic spherical triangle T(A; ~ B; ~ C~) whose arcs are represented by dual split quaternions.
Highlights
The dual hyperbolic unit sphere H~02 is the set of all time-like unit vectors in the dual Lorentzian space D31 with signature ( ; +; +)
In this paper we obtain the cosine hyperbolic and sine hyperbolic rules for a dual hyperbolic spherical triangle T (A~; B~; C~) whose arcs are represented by dual split quaternions
Dual hyperbolic spherical geometry which is studied by means of dual time-like unit vectors is analogous to real hyperbolic spherical geometry which is studied by means of real time-like unit vectors
Summary
The dual hyperbolic unit sphere H~02 is the set of all time-like unit vectors in the dual Lorentzian space D31 with signature ( ; +; +). In this paper we obtain hyperbolic sine and hyperbolic cosine rules by means of the correspondence between arcs of the dual hyperbolic spherical triangle on H~02 and dual split quaternions.
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