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A Note on the Linearity of Real-valued Functions with Respect to Suitable Metrics |
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| Authors: | Patrizio Frosini |
| Affiliation: | (1) Dipartimento di Matematica, Università di Bologna, Piazza Porta San Donato, 5, I-40126 Bologna, Italy;(2) Advanced Research Centre for Electronic Systems ‘Ercole De Castro’, Università di Bologna, Via Toffano, 2/2, I-40135 Bologna, Italy |
| Abstract: | In this paper we prove that for every real-valued Morse function φ on a smooth closed manifold ℳ and every neighborhood U of its critical points a suitable Riemannian metric μ U exists such that φ is linear outside U |
| Keywords: | linear function Riemannian metric |
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