In this paper we prove that for every real-valued Morse function $varphi$ on a smooth closed manifold $mathcal{M}$ and every neighborhood $U$ of its critical points a suitable Riemannian metric $mu_U$ exists such that $varphi$ is linear outside $U$.
A note on the linearity of real-valued functions with respect to suitable metrics / P. Frosini. - In: GEOMETRIAE DEDICATA. - ISSN 0046-5755. - STAMPA. - 108(1):(2004), pp. 105-110. [10.1007/s10711-004-8119-4]
A note on the linearity of real-valued functions with respect to suitable metrics
FROSINI, PATRIZIO
2004
Abstract
In this paper we prove that for every real-valued Morse function $varphi$ on a smooth closed manifold $mathcal{M}$ and every neighborhood $U$ of its critical points a suitable Riemannian metric $mu_U$ exists such that $varphi$ is linear outside $U$.File in questo prodotto:
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