Fabián AriasM. Malakhaltsev2026-03-222026-03-22202010.1134/s1995080220120070https://doi.org/10.1134/s1995080220120070https://andeanlibrary.org/handle/123456789/69513A contact structure on a three-dimensional manifold is a two-dimensional distribution on this manifold which satisfies the condition of complete non-integrability. If the distribution fails to satisfy this condition at points of some submanifold, we have a contact structure with singularities. The singularities of contact structures were studied by J. Martinet, B. Jakubczyk and M. Zhitomirskii. We consider a contact structure with singularities as a $$G$$ -structure with singularities, we find some topological and differential invariants of singularities of contact structure and establish their relation to the invariants found by B. Jakubczyk and M. Zhitomirskii.enGravitational singularityMathematicsSubmanifoldManifold (fluid mechanics)Contact geometryPure mathematicsDifferential geometryDistribution (mathematics)Topology (electrical circuits)Differential (mechanical device)article