In this paper we describe a new algorithm for the long-term numerical integration of the two-body problem, in which two particles interact under a Newtonian gravitational potential. Although analytical solutions exist in the unperturbed and weakly perturbed cases, numerical integration is necessary in situations where the perturbation is relatively strong. Kustaanheimo{Stiefel (KS) regularizati...

In this paper, based on the classical Yano’s formula, we first establish an optimal integral inequality for compact Lagrangian submanifolds in complex space forms, which involves Ricci curvature direction \(J\mathbf {H}\) and norm of covariant differentiation second fundamental form h, where J is almost structure \(\mathbf mean vector field. Second analogously, Legendrian Sasakian forms with \(...

In this article, we prove a Legendrian Whitney trick which allows for the removal of intersections between codimension-two contact submanifolds and submanifolds, assuming such smooth cancellation is possible. This technique applied to show existence h-principle embeddings with prescribed structure.