Lifts of calibrations and minimal surfaces on the tangent bundle of a Riemannian manifold
type: Item
instance of: scholarly article
title: Lifts of calibrations and minimal surfaces on the tangent bundle of a Riemannian manifold
zbMATH Open document ID: 0906.53040
author: Tran Viet Dung
author: Truong Chi Trung
published in: Vietnam Journal of Mathematics
publication date: 1999-02-09T00:00:00Z
review text: Let \(M\) be a Riemannian manifold. The authors study calibrations on the tangent bundle \(TM.\) Their main result states that if \(N\) is a connected, compact, \(k\)-dimensional surface in \(M\) for which there is a calibration \(\omega\) and if the horizontal lift of \(N\) into the tangent bundle \(TM\) is also compact, then \(\Pi^*\omega,\) the pull-back of the calibration, where \(\Pi:TM\to M\) is the natural projection, is a calibration of that horizontal lift and, consequently, the horizontal lift of \(N\) is homologically area-minimizing.
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 1143500
zbMATH Keywords: complete minimally immersed hypersurface
zbMATH Keywords: total scalar curvature
zbMATH Keywords: complex submanifolds
zbMATH Keywords: complete analytic immersions
reviewed by: Harold Parks
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1143500