On Imbedding Differentiable Manifolds in Euclidean Space

Notes on Differentiable Manifolds

Note on the Embedding of Manifolds in Euclidean Space

M. Hirsch and independently H. Glover have shown that a closed ¿-connected smooth «-manifold M embeds in R2n~> if Mo immerses in A*""*-1, jè2k and 2/gra — 3. Here Mo denotes M minus the interior of a smooth disk. In this note we prove the converse and show also that the isotopy classes of embeddings of M in i?a"-»' are in one-one correspondence with the regular homotopy classes of immersions of...

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...

On the Quaternionic Curves in the Semi-Euclidean Space E_4_2

In this study, we investigate the semi-real quaternionic curves in the semi-Euclidean space E_4_2. Firstly, we introduce algebraic properties of semi-real quaternions. Then, we give some characterizations of semi-real quaternionic involute-evolute curves in the semi-Euclidean space E42 . Finally, we give an example illustrated with Mathematica Programme.

Double Point Manifolds of Immersions of Spheres in Euclidean Space

Anyone who has been intrigued by the relationship between homotopy theory and diierential topology will have been inspired by the work of Bill Browder. This note contains an example of the power of these interconnections. We prove that, in the metastable range, the double point manifold a self-transverse immersion S n # R n+k is either a boundary or bordant to the real projective space RP n?k. ...