2015/03/23 by Agostino Prástaro, Prástaro, Agostino
Mathematics · #35Q30 #53D10 #53D12 #55N20 #57R45 #58J99 #FOS: Mathematics #General Mathematics (math.GM) #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.GM #msc:35Q30 #msc:53D10 #msc:53D12 #msc:55N20 #msc:57R45 #msc:58J99
paper · pdf · doi:10.48550/arxiv.1503.07851
40 pages, 2 figures
openalex publication_date 2015/03/23 · arxiv created 2015/11/16 · arxiv updated 2015/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02
It is proved that the Maslov index naturally arises in the framework of PDEs geometry. The characterization of PDE solutions by means of Maslov index is given. With this respect, Maslov index for Lagrangian submanifolds is given on the ground of PDEs geometry. New formulas to calculate bordism groups of (n-1)-dimensional compact sub-manifolds bording via n-dimensional Lagrangian submanifolds of a fixed 2n-dimensional symplectic manifold are obtained too. As a by-product it is given a new proof of global smooth solutions existence, defined on all ℝ3, for the Navier-Stokes PDE. Further, complementary results are given in Appendices concerning Navier-Stokes PDE and Legendrian submanifolds of contact manifolds.