A generating function of a complex Lagrangian cone in \(\mathbf{H}^n\)
type: Item
instance of: scholarly article
title: A generating function of a complex Lagrangian cone in \(\mathbf{H}^n\)
zbMATH Open document ID: 1530.53073
author: Norio Ejiri
published in: Communications in Analysis and Geometry
publication date: 2023-08-28T00:00:00Z
review text: In this interesting and technical paper, the author considers the space of multivalued branched minimal immersions of compact Riemann surfaces of genus \(\gamma\ge 2\) into \(\mathbb{R}^n\), proving that it is a complex analytic set and studying its irreducible components. The paper is organized into seven sections as follows: Introduction, A quaternion structure of \(L_{n,2\gamma}\times L_{n,2\gamma}\), Energy function, A complex isotropic submanifold in \(T^*L_{n,2\gamma}\), A special pseudo Kähler structure, Applications to minimal surfaces in flat tori, The deformation space of a holomorphic curve in a complex flat torus. Other papers by the author and his collaborators directly connected to this subject are: [Contemp. Math. 308, 101--144 (2002; Zbl 1071.58012); in: Contemporary aspects of complex analysis, differential geometry and mathematical physics. Proceedings of the 7th international workshop on complex structures and vector fields, Plovdiv, Bulgaria, August 31--September 4, 2004. Hackensack, NJ: World Scientific. 64--73 (2005; Zbl 1218.53066); in: Trends in differential geometry, complex analysis and mathematical physics. Proceedings of 9th international workshop on complex structures, integrability and vector fields, Sofia, Bulgaria, August 25--29, 2008. Hackensack, NJ: World Scientific. 74--82 (2009; Zbl 1190.53057); \textit{N. Ejiri} and \textit{M. Micallef}, Adv. Calc. Var. 1, No. 3, 223--239 (2008; Zbl 1163.58006); \textit{N. Ejiri} and \textit{T. Shoda}, Differ. Geom. Appl. 58, 177--201 (2018; Zbl 1388.53012); Mathematics 8, Art. No. 1693 (2020); \textit{N. Ejiri} and \textit{K. Tsukada}, Tokyo J. Math. 28, No. 1, 71--78 (2005; Zbl 1080.53041)].
reviewed by: Dorin Andrica
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 32Q15
Mathematics Subject Classification ID: 32Q65
zbMATH DE Number: 7732154
zbMATH Keywords: space of immersions
zbMATH Keywords: complex analytic set
zbMATH Keywords: complex period map
zbMATH Keywords: Morse index
MaRDI profile type: Publication
full work available at URL: cag.2022.v30.n9.a2
OpenAlex ID: W4385961589
DOI: 10.4310/CAG.2022.V30.N9.A2
description: scientific article; zbMATH DE number 7732154