Problems Of Submanifolds Of Almost Contact Manifolds

The theory of submanifolds is an important branch of differential geometry, which has a long history. It has important applications in many branches of mathematics and other disciplines. An almost contact metric manifold as a special kind of Riemannian manifold, which attracts the interest of geometricians.In this paper, we mainly study three kinds of problems on submanifolds of an al-most contact metric structure manifold and an almost contact metric 3-structure manifold. These problems are discussed in chapter 2, chapter 3 and chapter 4, respectively.In the first chapter, we present the background of an almost contact metric struc-ture manifold and an almost contact metric 3-structure manifold, also including the basic concepts and symbols.In the second chapter, we mainly study the invariant submanifolds of an almost contact metric structure manifold. Five equivalent conditions of totally geodesic are given. Finally, we give an example to support our main theorems.In the third chapter, we introduce the definition of a bi-slant submanifold of almost contact metric manifolds. Finally, some properties of bi-slant submanifolds are given.In the fourth chapter, we introduce the definition of a 3-pseudo-slant submanifold of almost contact metric 3-structure manifolds. An interesting example is constructed. At last, we present two conclusions.