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In the hypersphere soliton model, we investigate foliations related with thegeometry on a hypersphere $S^{3}$ which is described by $(\mu,\theta,\phi)$. Todo this, we introduce a projection from a northern hemi-hypersphere $S^{3}_{+}$to an equatorial volume $E^{3}$ which contains the center of $S^{3}$ and isdescribed in terms of the spherical coordinates of the solid sphere. Exploitingthe projection and the so-called scanning algorithm we study geometricalrelations between spherical shell foliation leave on the curved $S^{3}_{+}$ andthat on the flat equatorial volume $E^{3}$. We then elucidate the physicalmeaning of $\mu$ in $S^{3}$ of radius $\lambda$ by showing that $\mu$ plays therole of an auxiliary angle to fix the radius $\lambda\sin\mu$ of the $S^{2}$spherical shell sharing the center of $S^{3}(=S^{2}\times S^{1})$, at a givenangle $\mu$. Next, we study charge density profiles of nucleons which areformulated in terms of the angle $\mu$ in $S^{3}$. To be specific, we constructthe nucleon fractional three dimensional volumes and the correspondingfractional charges, which are spherically symmetric and possesses thenon-trivial distribution structures. In particular we find that, in the neutroncharge distribution, the positive and negative charges are confined inside andoutside the neutron core, respectively. We next observe that the proton andneutron charges do not leak out from the hypersphere soliton and thecharacteristic ratio of the hypersphere volume to the corresponding solidsphere one is given by the geometrical invariant. This invariant is also shownto originate from the projection and scanning algorithm procedure over theangle range $0\le\mu\le\pi$ of $S^{3}$.

Foliations, projections and nucleon charge profiles in hypersphere soliton model