Tohoku Mathematical Journal

Parallel mean curvature tori in $\mathbb{C}P^{2}$ and $\mathbb{C}H^{2}$

Katsuei Kenmotsu

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Abstract

We explicitly determine tori that have a parallel mean curvature vector, both in the complex projective plane and the complex hyperbolic plane.

Article information

Source
Tohoku Math. J. (2), Volume 70, Number 3 (2018), 475-485.

Dates
First available in Project Euclid: 21 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1537495357

Digital Object Identifier
doi:10.2748/tmj/1537495357

Mathematical Reviews number (MathSciNet)
MR3856777

Zentralblatt MATH identifier
06996538

Subjects
Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
Secondary: 53C55: Hermitian and Kählerian manifolds [See also 32Cxx]

Keywords
parallel mean curvature vector constant mean curvature surfaces in complex space forms

Citation

Kenmotsu, Katsuei. Parallel mean curvature tori in $\mathbb{C}P^{2}$ and $\mathbb{C}H^{2}$. Tohoku Math. J. (2) 70 (2018), no. 3, 475--485. doi:10.2748/tmj/1537495357. https://projecteuclid.org/euclid.tmj/1537495357


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