Abstract
Letx:M2→En be the immersion of a surfaceM2 in ann-dimensional Euclidean space. Letj and μ be the canonical isomorphism defined by the metricg ofM2 and by the canonical volume element ofM2, respectively. IfM2 carries a concircular tangent vector fieldX. then the following properties are proved: (i) The gaussian curvatureK ofM2 is identically zero. (ii) X defines an infinitesimal homothety onM2. (iii) The vector field (j−1 o μ) (X) is a Killing vector field.
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