Publication Cover
Applicable Analysis
An International Journal
Volume 41, 1991 - Issue 1-4
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Original Articles

On functions whose curves of steepest descent are straight lines

Pages 171-182 | Received 19 Sep 1990, Published online: 02 May 2007
 

Abstract

We consider functions such that their curves of steepest descent are straight lines. We prove that, along these curves, all principal curvatures of level surfaces of such functions satisfy a simple nonlinear ordinary differential equation. This result is used to get quantitative geometrical information on the level surfaces

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