## Advanced Studies in Pure Mathematics

### Constant mean curvature surfaces with $D_4$-singularities

#### Abstract

We study $D_4$-singularities of constant mean curvature (CMC) surfaces in Riemannian and semi-Riemannian spaceforms. We will give criteria for $D_4^{-}$-singularities, which are related to the Hopf differential. We also show the non-existence of (spacelike) CMC surfaces with $D_4^+$-singularities.

#### Article information

Dates
Received: 18 January 2016
Revised: 28 March 2017
First available in Project Euclid: 4 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1538618981

Digital Object Identifier
doi:10.2969/aspm/07810345

Mathematical Reviews number (MathSciNet)
MR3839953

Zentralblatt MATH identifier
1420.53068

#### Citation

Ogata, Yuta; Teramoto, Keisuke. Constant mean curvature surfaces with $D_4$-singularities. Singularities in Generic Geometry, 345--363, Mathematical Society of Japan, Tokyo, Japan, 2018. doi:10.2969/aspm/07810345. https://projecteuclid.org/euclid.aspm/1538618981