On convolution surfaces in Euclidean 3-space | Zendy

Selin AYDÖNER | Zendy; Kadri Arslan | Zendy

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On convolution surfaces in Euclidean 3-space

Author(s) -

Selin AYDÖNER,

Kadri Arslan

Publication year - 2018

Publication title -

journal of mathematical sciences and modelling

Language(s) - English

Resource type - Journals

ISSN - 2636-8692

DOI - 10.33187/jmsm.424796

Subject(s) - convolution (computer science) , surface (topology) , paraboloid , gaussian curvature , surface of revolution , mathematics , curvature , space (punctuation) , euclidean geometry , parametric surface , parametric statistics , euclidean space , pure mathematics , mathematical analysis , geometry , computer science , artificial intelligence , artificial neural network , operating system , statistics

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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