On Finsler transnormal functions |
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| Institution: | 1. Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, 05508-090 São Paulo, Brazil;2. Departamento de Matemática CCET-UFMA, Cidade Universitária Dom Delgado, Av. dos Portugueses, 1966, Bacanga, CEP 65080-805 São Luís, MA, Brazil |
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| Abstract: | In this note we discuss a few properties of transnormal Finsler functions, i.e., the natural generalization of distance functions and isoparametric Finsler functions. In particular, we prove that critical level sets of an analytic transnormal function are submanifolds, and the partition of M into level sets is a Finsler partition, when the function is defined on a compact analytic manifold M. |
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| Keywords: | Finsler foliations Transnormal functions Morse-Bott functions |
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