Startseite Caustics of pseudo-spherical surfaces in the Euclidean 3-space
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Caustics of pseudo-spherical surfaces in the Euclidean 3-space

  • Keisuke Teramoto ORCID logo EMAIL logo
Veröffentlicht/Copyright: 27. Juni 2023

Abstract

We study geometric properties of caustics of pseudo-spherical surfaces, that is, surfaces with constant negative Gaussian curvature -1 in the Euclidean 3-space 3 . We investigate the Gaussian and the mean curvature of caustics of pseudo-spherical surfaces. Moreover, a certain condition required for the caustics to be minimal surfaces is derived.

MSC 2020: 53A05; 53A10; 57R45

Communicated by Karin Melnick


Award Identifier / Grant number: JP19K14533

Award Identifier / Grant number: JP22K13914

Award Identifier / Grant number: JP20H01801

Award Identifier / Grant number: JP22KK0034

Award Identifier / Grant number: JPJSBP1 20190103

Funding statement: The author was partially supported by JSPS KAKENHI Grant Numbers JP19K14533, JP22K13914, JP20H01801 and JP22KK0034 and the Japan–Brazil bilateral project JPJSBP1 20190103.

Acknowledgements

The author would like to thank Professors Shoichi Fujimori, Wayne Rossman and Kentaro Saji for fruitful discussions and comments. He also thanks Shin Kaneda and Masahiro Kawamata for their valuable comments. The author thanks the referees for useful suggestions and comments.

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Received: 2022-11-19
Revised: 2023-03-20
Published Online: 2023-06-27
Published in Print: 2024-01-01

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