  The purpose of this contribution is to show how a nuclear field theory
follows naturally from the structure of four-dimensional Riemannian geometry. A
Yang-Mills field is introduced by constructing fibres that include all possible
exchanges of spin, parity and charge such that the collective quantum numbers
remain the same. In this way O(4) internal symmetry transformations are found
and a connection is obtained by exponentiation of a CP-invariant operator C
associated with the ground state. The metric is Calabi-Yau and Einstein. Carbon
13 is chosen as an example because it is the lightest nucleus to exhibit small
spin mutations even though there is no deformation parameter in the O(4)
commutation relations. Instead a supersymmetric transformation replaces a
quantum group. Mirror symmetry is also discussed.
