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Decomposing the Higgs potential $\mathcal{V}_{higgs}$ of next - to - MinimalSupersymmetric Standard Model (n-MSSM) \ as the sum of three contributions like$\mathcal{V}_{ch}+\mathcal{V}_{kah}+\mathcal{V}_{expl}$ and assuming the twofollowing things: $\left( a\right) $ $\mathcal{V}_{higgs}$ dominated by$\mathcal{V}_{ch}$ coming from the chiral sector of supersymmetry:$\mathcal{V}_{ch}=\left \vert \mathrm{\nu }\right \vert ^{2}\mathcal{U}$ with$\left \vert \mathrm{\nu }\right \vert $ large and $\frac{\mathrm{r}}{\left\vert \mathrm{\nu }\right \vert }<<1$; and $\left( b\right) $ replacing thechiral down Higgs superfield doublet $\left( \boldsymbol{H}_{d}\right) ^{i}$ ofn-MSSM by a chiral anti-doublet $\left( \boldsymbol{\Phi}_{d}\right) _{i}$; wederive the explicit geometry of the Higgs fields in the ground state $\left\vert \Sigma _{higgs}\right \rangle $ found to be given by two intersectingconifolds. We show as well that the property $\tan \beta _{susy}=1$ living atsingularity $r=0$ is a supersymmetric signal; and deviation away reads in termsof the Kahler parameter $r$ and the $\vartheta_{_{W}}$- Weinberg angle as $\tan\beta \simeq1+\frac{\mathrm{r}}{2\left \vert \mathrm{\nu }\right \vert}\sin^{2}\vartheta _{_{W}}$. Other related issues are also studied.

Geometry of the Ground State of Higgs Fields in Next-to-MSSM