On convolution surfaces in Euclidean 3-space

Year 2018, Volume: 1 Issue: 2, 86 - 92, 30.09.2018

Selin Aydöner Kadri Arslan

https://doi.org/10.33187/jmsm.424796

Cited By: 1

Abstract

In the present paper we study with the convolution surface $C=M\star N$ of a paraboloid $M\subset \mathbb{E}^{3}$ and a parametric surface $N\subset \mathbb{E}^{3}$. We take some spacial surfaces for $N$ such as, surface of revolution, Monge patch and ruled surface and calculate the Gaussian curvature of the convolution surface $C$. Further, we give necessary and sufficient conditions for a convolution surface $C$ to become flat.

Keywords

Minkowski sum, Convolution of surfaces, Flat surfaces, Gaussian curvature, Second fundamental form

References

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