Some notes on differentiable manifolds with almost contact structures

Notes on Differentiable Manifolds

Lecture Notes on Differentiable Manifolds

1. Tangent Spaces, Vector Fields in R and the Inverse Mapping Theorem 1 1.1. Tangent Space to a Level Surface 1 1.2. Tangent Space and Vectors Fields on R 2 1.3. Operator Representations of Vector Fields 3 1.4. Integral Curves 4 1.5. Implicitand Inverse-Mapping Theorems 5 2. Topological and Differentiable Manifolds 9 3. Diffeomorphisms, Immersions, Submersions and Submanifolds 9 4. Fibre Bundle...

Notes on some classes of 3-dimensional contact metric manifolds

A review of the geometry of 3-dimensional contact metric manifolds shows that generalized Sasakian manifolds and η-Einstein manifolds are deeply interrelated. For example, it is known that a 3-dimensional Sasakian manifold is η-Einstein. In this paper, we discuss the relationships between several special classes of 3-dimensional contact metric manifolds which are generalizations of 3-dimensiona...

Contact Structures on 5–manifolds

Using recent work on high dimensional Lutz twists and families of Weinstein structures we show that any almost contact structure on a 5–manifold is homotopic to a contact structure.

DIFFERENTIABLE STRUCTURES 1. Classification of Manifolds

(1) Classify all spaces ludicrously impossible. (2) Classify manifolds only provably impossible (because any finitely presented group is the fundamental group of a 4-manifold, and finitely presented groups are not able to be classified). (3) Classify manifolds with a given homotopy type (sort of worked out in 1960’s by Wall and Browder if π1 = 0. There is something called the Browder-Novikov-Su...