On the Quaternion Transformation and Field Equations in Curved Space-Time

In this paper, we use four-dimensional quaternionic algebra to describing space-time field equations in curvature form. The transformation relations of a variable are established with the help basis transformations quaternion algebra. We deduced covariant derivative that explains how components vary scalar and vector fields.The metric tensor geodesic equation also discussed line element curved space-time. Moreover, an expression for Riemannian Christoffel terms tensor. have form Einstein-field-like which shows equivalence between matter geometry.