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Transnormal Functions and Focal Varieties on Finsler Manifolds

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Abstract

In this paper, we study transnormal functions and their level sets and focal varieties on complete Finsler manifolds. We prove that the focal varieties of a \(C^{2}\) transnormal function are smooth submanifolds and each regular level set is a tube over either of the focal varieties.

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Authors and Affiliations

  1. School of Mathematical Sciences, Tongji University, Shanghai, 200092, China

    Yali Chen & Qun He

  2. School of Mathematics and Statistics, Anhui Normal University, Wuhu, Anhui, 241000, China

    Yali Chen

Authors
  1. Yali Chen
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  2. Qun He
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Correspondence to Yali Chen.

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Project supported by AHNSF (No.2108085MA11), NSFC (No.12261034).

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Chen, Y., He, Q. Transnormal Functions and Focal Varieties on Finsler Manifolds. J Geom Anal 33, 128 (2023). https://doi.org/10.1007/s12220-022-01184-8

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  • DOI: https://doi.org/10.1007/s12220-022-01184-8

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