Kaehler manifolds isometrically immersed in Euclidean space

A Menger Redux: Embedding Metric Spaces Isometrically in Euclidean Space

We present geometric proofs of Menger’s results on isometrically embedding metric spaces in Euclidean space. In 1928, Karl Menger [6] published the proof of a beautiful characterization of those metric spaces that are isometrically embeddable in the ndimensional Euclidean space E. While a visitor at Harvard University and the Rice Institute in Houston during the 1930-31 academic year, Menger ga...

Lecture on Kaehler manifolds

Lectures on Geodesics in the Space of Kaehler Metrics, Lecture 3: Hrma, Hcma and Toric Kaehler Manifolds

It is very hard to find computable examples of geodesics in the space of Kaehler metrics. It seems that they come in two types: (i) geodesics of toric Kaehler metrics, the topic of Lecture 2; (iii) geodesics coming from special test configurations and Hele-Shaw flows. Besides Donaldson’s construction (reviewed in §1) there are not many examples of geodesic rays. Almost the only other explicit e...

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. ...

Embeddings and Immersions of Manifolds in Euclidean Space

The problem of computing the number of embeddings or immersions of a manifold in Euclidean space is treated from a different point of view than is usually taken. Also, a theorem dealing with the existence of an embedding of Mm in ä ¡s given. Introduction. This paper studies the existence and classification of differential immersions and embeddings of a differentiable manifold into Euclidean spa...