The amalgamatic curvature and the orthocurvatures of three dimensional hypersurfaces in the Euclidean space (Q2834174)
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scientific article; zbMATH DE number 6656670
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The amalgamatic curvature and the orthocurvatures of three dimensional hypersurfaces in the Euclidean space |
scientific article; zbMATH DE number 6656670 |
Statements
The amalgamatic curvature and the orthocurvatures of three dimensional hypersurfaces in the Euclidean space (English)
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25 November 2016
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principal curvatures
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scalar curvature
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shape operator
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amalgamatic curvature
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absolutely umbilical hypersurfaces
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ladder of power means
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orthocurvatures
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0.8644488
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0.86305416
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0.8565967
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0.85578465
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0.8522873
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0.85140866
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Recently, a new curvature, called \textit{amalgamatic}, was introduced by the present author. This curvature can be described as the arithmetic mean of the harmonic means of all the pairs of absolute values of principal curvatures and hence, is a construction similar to the Riemannian scalar curvature. The present paper is a detailed study of this curvature for three-dimensional hypersurfaces in \(\mathbb{R}^4\).
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