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

Published online by Cambridge University Press:  20 January 2009

Cornel Pintea
Cornel Pintea
Affiliation:
“Babeş-Bolyai” University, Department of Mathematics, Str. Kogălniceanu 1, 3400 CLUJ-NAPOCA, Romania E-mail: [email protected]
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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, n → Rm, has infinitely many critical points for suitable choices of the numbers m, n, k.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 41 , Issue 1 , February 1998 , pp. 197 - 205
Copyright
Copyright © Edinburgh Mathematical Society 1998

References

REFERENCES

1.Andrica, D. and Pintea, C., Critical points of vector-valued functions (Proceedings of the 24th National Conference of Geometry and Topology, 07 5–9, 1994, Romania, University of Timisoara, 1996).Google Scholar
2.Berstein, I., On the Lusternik-Schnirelmann category of Grassmannians, Math. Proc. Cambridge Philos. Soc. 79 (1976), 129–134.CrossRefGoogle Scholar
3.Milnor, J. W. and Stasheff, J. D., Characteristic classes (Princeton, New Jersey, 1974).CrossRefGoogle Scholar
4.Oproiu, V., Some non-embedding theorems for the Grassmann manifolds, Proc. Edinburgh Math. Soc. 20 (1976–1977), 177–185.CrossRefGoogle Scholar
5.Palais, R. S. and Terag, C. L., Critical Point Theory and Submanifold Geometry (Springer-Verlag, Lecture Notes in Mathematics, 1988).CrossRefGoogle Scholar
6.Takens, F., The minimal number of critical points of a function on a compact manifold and the Lusternik-Schnirelmann Category, Invent. Math. 6 (1968), 197–244.CrossRefGoogle Scholar