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JP Journal of Geometry and Topology

JP Journal of Geometry and Topology
Volume 21, Issue 3, Pages 247 - 253 (August 2018)
http://dx.doi.org/10.17654/GT021030247

ON TOTALLY UMBILICAL ISOMETRIC IMMERSION WITH A SPECIAL KIND OF LIOUVILLE’S METRIC IN THE R³ SPACE

Alexander Pigazzini

Abstract:

The aim of this short article is to investigate the possibility of existence of totally umbilical isometric immersions in R³with isothermal parametrization and harmonic metric.

Keywords and phrases:

harmonic metric, isothermal coordinates, Liouvilles metric, totally umbilical immersions.

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