  The paper focuses on finding out several physical quantities to exert an
influence on the spatial parameters of complex-octonion curved space, including
the metric coefficient, connection coefficient, and curvature tensor. In the
flat space described with the complex octonions, the radius vector is combined
with the integrating function of field potential to become a composite radius
vector. And the latter can be considered as the radius vector in a flat
composite-space (a function space). Further it is able to deduce some formulae
between the physical quantity and spatial parameter, in the complex-octonion
curved composite-space. Under the condition of weak field approximation, these
formulae infer a few results accordant with the General Theory of Relativity.
The study reveals that it is capable of ascertaining which physical quantities
are able to result in the warping of space, in terms of the curved
composite-space described with the complex octonions. Moreover, the method may
be expanded into some curved function spaces, seeking out more possible
physical quantities to impact the bending degree of curved spaces.
