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Abstract

We prove that exponentially harmonic morphisms are precisely the Riemannian submersions with minimal fibres. 1991 Mathematics Subject Classification 58E20.
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We study the exponential stress energy associated to an exponentially harmonic map between Riemannian manifolds. We prove three equivalent statements for a horizontally weakly conformal exponentially harmonic map between Riemannian manifolds. We also investigate the stability of exponentially harmonic maps.
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Properties of steady compressible flow for which geometric constraints have been placed on the potential function are derived, under hypotheses on the flow density and the singular set. Some related unconstrained problems are also considered, including the estimation of a class of fields having nonzero vorticity.