Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

A measure of non-immersability of the Grassmann manifolds in some euclidean spaces

Cornel Pinteaa1

a1 “Babeş-Bolyai” University, Department of Mathematics, Str. Kogălniceanu 1, 3400 CLUJ-NAPOCA, Romania E-mail: cpintea@math.ubbcluj.ro

Let Gk, n, be the Grassmann manifold consisting in all non-oriented k-dimensional vector subspaces of the space Rk+n. In this paper we will show that any differentiable mapping f: Gk, nRm, has infinitely many critical points for suitable choices of the numbers m, n, k.

(Received April 19 1996)