Contact and equivalence of submanifolds of homogeneous spaces

Abstract

Publisher Summary This chapter discusses the contact and equivalence of submanifolds of homogeneous spaces. The chapter states a generalization of Frobenius theorem to differential systems defined by contact elements of higher order. This theorem is the main tool in the proof of equivalence theorem. The chapter proves the equivalence theorem. The chapter provides a necessary and sufficient condition for a submanifold S ⊂ M to be an open set of an orbit of a Lie subgroup L of G . This theorem can be generalized to characterize the submanifolds S of M that are locally invariant by the action of a Lie subgroup L of G and that are fibered by the orbits of L which meet S . The chapter also discusses the curves in ℝ 3 .