Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# The Third Laplace-Beltrami Operator of the Rotational Hypersurface in 4-Space

Version 1 : Received: 9 June 2018 / Approved: 11 June 2018 / Online: 11 June 2018 (12:35:51 CEST)

How to cite: Güler, E. The Third Laplace-Beltrami Operator of the Rotational Hypersurface in 4-Space. Preprints 2018, 2018060159 (doi: 10.20944/preprints201806.0159.v1). Güler, E. The Third Laplace-Beltrami Operator of the Rotational Hypersurface in 4-Space. Preprints 2018, 2018060159 (doi: 10.20944/preprints201806.0159.v1).

## Abstract

We consider rotational hypersurface in the four dimensional Euclidean space. We calculate the mean curvature and the Gaussian curvature, and some relations of the rotational hypersurface. Moreover, we define the third Laplace-Beltrami operator and apply it to the rotational hypersurface.

## Subject Areas

4-space; the third Laplace-Beltrami operator; rotational hypersurface; Gaussian curvature; mean curvature

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