Vol. 319, No. 1, 2022

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
On the multiplicity of umbilic points

Marco Antônio do Couto Fernandes and Farid Tari

Vol. 319 (2022), No. 1, 99–127
Abstract

We introduce an invariant of umbilic points on surfaces in Euclidean or Minkowski 3-space that counts the maximum number of stable umbilic points they can split up under local deformations of the surfaces. We call that number the multiplicity of the umbilic point and establish its properties.

PDF Access Denied

We have not been able to recognize your IP address 34.236.191.0 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords
umbilic points, lines of principal curvature, multiplicity, singularities
Mathematical Subject Classification
Primary: 53A05, 53A35, 53A55
Secondary: 58K05
Milestones
Received: 8 September 2021
Revised: 21 January 2022
Accepted: 21 January 2022
Published: 28 August 2022
Authors
Marco Antônio do Couto Fernandes
Instituto de Ciências Matemáticas e de Computação
University of São Paulo
São Carlos, SP
Brazil
Farid Tari
Instituto de Ciências Matemáticas e de Computação
University of Sao Paulo
São Carlos, SP
Brazil