Variational geometry for surfaces in conformally flat space

Authors: NAJMA MOSADEGH, ESMAIEL ABEDI

Abstract: In this paper, it is shown that a closed surface in 3-dimensional harmonic conformally flat space is minimal if the sign of the mean curvature does not change. Also, it is determined that the critical point of mean curvature functional of the surface is homeomorphic to the sphere.

Keywords: Conformally flat spaces, variational aspect

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