ORCID

https://orcid.org/0000-0002-7437-5046

Abstract

In this note a definition of umbilic point at infinity is proposed, at least for surfaces that are homogeneous polynomial graphs over a plane in Euclidean 3-space. This is a stronger definition than that of Toponogov in his study of complete convex surfaces, and allows one to distinguish between different umbilic points at infinity. It is proven that all such umbilic points at infinity are isolated, that they occur in pairs and are the zeroes of the projective extension of the third fundamental form, as developed in Guilfoyle and Ortiz-Rodríguez (Math Proc R Ir Acad 123A(2), 63–94, 2023). A geometric interpretation for the definition is that an umbilic point at infinity occurs when the tangent to the level set at infinity is also an asymptotic direction at infinity

Disciplines

Algebra | Geometry and Topology | Mathematics | Physical Sciences and Mathematics

DOI

10.1007/s13366-024-00740-3

Full Publication Date

6-4-2024

Publication Details

Beiträge zur Algebra und Geometrie. © The Author(s) 2024

Publisher

Springer

Funder Name 1

Irish Research eLibrary (IReL)

Resource Type

journal article

Resource Version

http://purl.org/coar/version/c_970fb48d4fbd8a85

Access Rights

open access

Open Access Route

Hybrid Open Access

License Condition

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Alternative Identifier

https://link.springer.com/article/10.1007/s13366-024-00740-3

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