On convolution surfaces in Euclidean 3-space

ISSN: 2636-8692
Yayın Aralığı: Yılda 3 Sayı
Başlangıç: 2018
Yayıncı: Mahmut AKYİĞİT

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,

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