Finite type of the pedal of revolution surfaces in $E^{3}$

Mohamed Abdelatif; Hamdy Nour alldeen; Hassan Saoud; Saleh Suorya

doi:10.4134/JKMS.j150336

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2016; 53(4): 909-928

Printed July 1, 2016

https://doi.org/10.4134/JKMS.j150336

Finite type of the pedal of revolution surfaces in $E^{3}$

Mohamed Abdelatif, Hamdy Nour alldeen, Hassan Saoud, and Saleh Suorya

Assiut University, Assiut University, Assiut University, Assiut University

Abstract

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Abstract

Chen and Ishikawa studied the surfaces of revolution of the polynomial and the rational kind of finite type in Euclidean $3$-space $ E^{3}$ \cite{3ch2}. Here, the pedal of revolution surfaces of the polynomial and the rational kind are discussed. Also, as a special case of general revolution surfaces, the sphere and catenoid are studied for the kind of finite type.

Keywords: pedal surfaces, revolution surfaces, finite type

MSC numbers: 53B25, 53C40