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We implement type-II seesaw dominance for neutrino mass and baryogenesisthrough heavy scalar triplet leptogenesis in a class of minimalnon-supersymmetric SO(10) models where matter parity as stabilising discretesymmetry as well as WIMP dark matter (DM) candidates are intrinsic predictionsof the GUT symmetry. We also find modifications of relevant CP-asymmetryformulas in such minimal models. Baryon asymmetry of the universe as solutionsof Boltzmann equations is further shown to be realized for both normal andinverted mass orderings in concordance with cosmological bound and best fitvalues of the neutrino oscillation data including $\theta_{23}$ in the secondoctant and large values of leptonic Dirac CP-phases. Type-II seesaw dominanceis at first successfully implemented in two cases of spontaneous SO(10)breakings through SU(5) route where the presence of only one non-standard Higgsscalar of intermediate mass $\sim 10^9-10^{10}$ GeV achieves unification. Lowervalues of the SU(5) unification scales $\sim 10^{15}$ GeV are predicted tobring proton lifetimes to the accessible ranges of Super-Kamiokande andHyper-Kamiokande experiments. Our prediction of WIMP DM relic density in eachmodel is due to a $\sim$ TeV mass matter-parity odd real scalar singlet($\subset {16}_H \subset$ SO(10)) verifiable by LUX and XENON1T experiments.This DM is also noted to resolve the vacuum stability issue of the standardscalar potential. When applied to the unification framework of M. Frigerio andT. Hambye, in addition to the minimal fermionic triplet DM solution of $2.7$TeV mass, this procedure of type-II seesaw dominance and triplet leptogenesisis also found to make an alternative prediction of triplet fermion plus realscalar singlet DM at the TeV scale.

Triplet Leptogenesis, Type-II Seesaw Dominance, Intrinsic Dark Matter, Vacuum Stability and Proton Decay in Minimal SO(10) Breakings