• SOME THEOREMS DUE TO EPSTEIN AND SCHWARZENBERGER

Hamdi M. Genedi*, K. A. M. Kotb

Abstract


Epstein and Schwarzenberger said that if P_n is real projective space of dimension n, and f is homeomorphism of P_n into Euclidean m –space, then f is an embedding if it is differentiable and regular. They proved two theorems: (I) if n=2k,k>1 but it is not a power of 2, then P_n can be embedded in (2n-1) - space. (II) if n=4k+1, k>1 but it is not a power of 2, then P_n can be embedded in (2n-2)- space. In this paper we prove these two theorems in the complex case.

Keywords


Embeddings, Complex projective spaces, Normal bundle, Complex vector bundle and Chern classes.

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