Lifts of calibrations and minimal surfaces on the tangent bundle of a Riemannian manifold
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.
complete minimally immersed hypersurface
scientific article; zbMATH DE number 1143500
scientific article