Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

The notions of a Jacobi field and of conjugate points appearnaturally while considering second order optimality conditions invariational problems. At the lecture I will study the geometric nature ofJacobi fields and their relation with Euler-Lagrange equations. Inparticular I will show that existence of conjugate points is equivalentwith existence of the null space of the symmetric form defined by thesecond variation for a wide class of variational problems.