We establish a link between the CR geometry of real analytic submanifolds in I C and the geometric PDE theory. The main idea of our approach is to consider biholomorphisms of a Levi-nondegenerate real analytic Cauchy-Riemann manifold M as poinwise symmetries of a second order holomorphic PDE system defining the Segre family of M. This allows to employ the well-elaborated PDE tools in order to s...

‎we prove that there do not exist totally contact umbilical‎ ‎proper slant lightlike submanifolds of indefinite sasakian manifolds other than totally contact geodesic‎ ‎proper slant lightlike submanifolds‎. ‎we also prove that there do‎ ‎not exist totally contact umbilical proper slant lightlike‎ ‎submanifolds of indefinite sasakian space forms‎.

In this article, we derived an equality for CR-warped product in a complex space form which forms the relationship between gradient and Laplacian of warping function second fundamental form. We necessary conditions submanifolds Ka¨hler manifold to be Einstein impact Ricci soliton. Some classification by using Euler–Lagrange equation, Dirichlet energy Hamiltonian is given. also derive some chara...