Differentiable manifolds admitting complex distributions

Manifolds admitting stable forms

Special geometries defined by a class of differential forms on manifolds are again in the center of interests of geometers. These interests are motivated by the fact that such a setting of special geometries unifies many known geometries as symplectic geometry and geometries with special holonomy [Joyce2000], as well as other geometries arised in the M-theory [GMPW2004], [Tsimpis2005]. A series...

Notes on Differentiable Manifolds

Manifolds of Differentiable Densities

We develop a family of infinite-dimensional (i.e. non-parametric) manifolds of probability measures. The latter are defined on underlying Banach spaces, and have densities of class Ck b with respect to appropriate reference measures. The case k = ∞, in which the manifolds are modelled on Fréchet spaces, is included. The manifolds admit the Fisher-Rao metric and the dually flat geometry of Amari...

Stable Equivalence of Differentiable Manifolds

A natural question, of great generality, various special forms of which are often asked in differential topology, is the following: Let Mi, Mi be differentiable w-manifolds, : M\—»M2 a continuous map which is a homotopy equivalence between M\ and M2. When is there a differentiable isomorphism <3>: Mi—> M2 in the same homotopy class as 0? For example, there is the Poincaré Conjecture which po...

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...