On slant surfaces
type: Item
instance of: scholarly article
title: On slant surfaces
zbMATH Open document ID: 1013.53038
author: Bang-Yen Chen
published in: Taiwanese Journal of Mathematics
publication date: 2003-06-20T00:00:00Z
review text: Slant immersions in complex geometry were defined by the author [Geometry of slant submanifolds, Leuven: Kath. Univ. Leuven, Dept. Math. 123 p. (1990; Zbl 0716.53006)] as a generalisation of both holomorphic immersions and totally real immersions. In the present paper the author considers a slant submanifold \(M\) of a Kählerian \(m\)-manifold \(M^2(4\varepsilon)\) with a constant holomorphic sectional curvature \(4\varepsilon\) and proves the inequality \[ H^2(p) \geq 2K(p) - 2(1+3\cos^2\theta)\varepsilon, \quad p\in M, \] where \(H\) and \(K\) are the mean curvature and the Gauss curvature of \(M\), respectively, and \(\theta\) is the slant angle. Then he proves that proper surfaces in \(\mathbb{C}^2\) are minimal if and only if they are special slant. Finally, he determines proper slant surfaces incomplex space forms satisfying the equality case of the above inequality.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 1339905
zbMATH Keywords: slant submanifods
zbMATH Keywords: Kählerian manifolds
zbMATH Keywords: minimal surfaces
reviewed by: Radu Miron
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.11650/twjm/1500407091
OpenAlex ID: W4253806018
Wikidata QID: Q126007746
DOI: 10.11650/TWJM/1500407091
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description: scientific article; zbMATH DE number 1339905