The incorrect statement among the following for sigma- ($\sigma$) and pi- ($\pi$) bonds formed between two carbon atoms is:

To identify the incorrect statement, we analyze the properties of sigma and \pi bonds based on chemical principles and the provided sources:

1. Strength: A sigma bond is stronger than a \pi bond because it is formed by the head-on overlap of atomic orbitals, which results in a greater extent of overlapping .
2. Bond Energies: According to the sources, the bond enthalpy of a carbon-carbon single bond (which is a sigma bond) is approximately 347 kJ/mol . In a double bond, the \pi bond is weaker, with a bond enthalpy of approximately 284 kJ/mol . Therefore, the statement claiming the sigma bond is 264 kJ/mol and the \pi bond is 347 kJ/mol is incorrect because it misstates the values and implies the \pi bond is stronger.
3. Rotation: Sigma bonds allow for free rotation of atoms around the bond axis because the electron distribution is symmetrical around the internuclear axis . However, rotation about a \pi bond is restricted because it would disrupt the parallel orientation of p-orbitals required for sideways overlap .
4. Directionality: Sigma bonds are formed by axial overlap along the internuclear axis and determine the geometry and primary direction of the bond between atoms . Pi bonds are formed by lateral overlap and do not primarily determine the direction of the bond .