Diagonal lift in the tensor bundle and its applications.
type: Item
instance of: scholarly article
title: Diagonal lift in the tensor bundle and its applications.
zbMATH Open document ID: 1034.53016
DOI: 10.1016/S0096-3003(02)00305-3
published in: Applied Mathematics and Computation
publication date: 2003-07-30T00:00:00Z
review text: Let \((M,g)\) be a Riemannian manifold and \(T^1_q(M)\) the bundle of tensors of type \((1,q)\) on~\(M\). The authors introduce a Riemannian metric \({}^Dg\) on~\(T^1_q(M)\), completely determined by the metric~\(g\) on~\(M\), which they call the \textit{diagonal lift of~\(g\).} Its definition is similar to that of the well-known Sasaki metric on~\(TM\). They compute the Levi-Civita connection of~\({}^Dg\) and they investigate under which conditions the complete or horizontal lift to~\(T^1_q(M)\) of a Killing vector field on~\(M\) is Killing for the metric~\({}^Dg\).
reviewed by: Eric Boeckx
Mathematics Subject Classification ID: 53B20
zbMATH DE Number: 1957157
zbMATH Keywords: tensor bundle
zbMATH Keywords: diagonal lift
zbMATH Keywords: Killing vector fields
author: Nejmi Ceng{i}z
author: A. Salimov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1957157