Journal of Mathematical Sciences and Modelling (Sep 2018)

On convolution surfaces in Euclidean 3-space

  • Kadri Arslan,
  • Selin Aydöner

DOI
https://doi.org/10.33187/jmsm.424796
Journal volume & issue
Vol. 1, no. 2
pp. 86 – 92

Abstract

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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.

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