Complex manifolds modeled on a complex Minkowski space
type: Item
instance of: scholarly article
title: Complex manifolds modeled on a complex Minkowski space
zbMATH Open document ID: 0832.53055
author: Tadashi Aikou
published in: Journal of Mathematics of Kyoto University
publication date: 1996-02-26T00:00:00Z
review text: The author studies some problems of the differential geometry of complex Finsler manifolds. He defines a complex Finsler metric on \(\mathbb{C}^n\) as a function \(f : \mathbb{C}^n \to R\) having the properties: i) \(f(\xi) \geq 0\), ii) \(f(\xi)\) is \(C^\infty\) on \(\mathbb{C}^n \setminus \{0\}\) and continuous on \(\mathbb{C}^n\), iii) \(f(\lambda \xi) = |\lambda|^2 f(\xi)\), \(\lambda \in \mathbb{C}\), and iv) the Hermitian matrix \(|{\partial^2 f/\partial \xi^\alpha\partial \overline {\xi}^\beta} |\) is positive definite. This notion is extended to complex manifolds \(M\) using the tangent bundle TM. Thus, a complex Finsler manifold is a pair \(^\mathbb{C} F^n = (M,F)\), where \(M\) is a complex manifold and \(F\) is a complex Finsler metric on \(M\). For \(^\mathbb{C} F^n\) the notion of Finsler connection \(\nabla\), the Kähler condition for \(\nabla\) and complex manifolds modeled on a complex Minkowski space are studied.
reviewed by: Radu Miron
Mathematics Subject Classification ID: 53C60
Mathematics Subject Classification ID: 53C56
zbMATH DE Number: 784737
zbMATH Keywords: complex Finsler manifold
zbMATH Keywords: Finsler connection
zbMATH Keywords: Kähler condition
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250518843
OpenAlex ID: W1553404770
DOI: 10.1215/KJM/1250518843
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description: scientific article; zbMATH DE number 784737