On totally umbilical isometric immersions with a special kind of Liouville metric in the R3 space
Alexander Pigazzini
TL;DR
This paper investigates the existence of totally umbilical isometric immersions in three-dimensional space with specific harmonic and isothermal metric properties, contributing to differential geometry understanding.
Contribution
It explores the possibility of such immersions with Liouville metrics in R^3, providing new insights into their geometric structure.
Findings
No such immersions exist under the specified conditions.
Characterization of harmonic Liouville metrics in R^3.
Conditions for totally umbilical isometric immersions with special metrics.
Abstract
The aim of this short article is to investigate the possibility of existence of totally umbilical isometric immersions in R^3 with isothermal parametrization and harmonic metric.
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