Consider a space constrained by a matrix of functions [M] and containing a
physical system represented by a vector array of p-forms |omega>. The Matrix
acting as a linear map on |omega> produces a vector array |sigma>. The
restricted domain on which the determinant of the matrix is non-zero enables the
matrix to be used as a basis Frame for vectors on the space. The existence of
an Inverse Frame permits the definition of a linear connection, such that the
exterior derivative of any matrix column is a linear combination of the matrix
A second exterior derivative of the Frame will generate the curvature properties
of the restricted domain. In effect, the matrix of functions [M] makes a
statement about the geometric properties of the restricted space, and in a
manner that does not depend upon |omega>.
The map is written symbollically as
The Connection [C] is defined as
Exterior differentiation of the map gives d(map)
A second exterior differentiation yields
The term [Theta]|omega> represents a Curvature effect.
IF all functions are C2, the double exterior derviative terms vanish.
IT would appear that gravitational effects (due to curvature - [Theta]|omega>)
can be balanced out by Coriolis -2[C]|d(omega)>
See the notes in the download below.