Constant Angle Ruled Surfaces with a Pointwise 1-Type Gauss Map

Vladimir Baltić, Kemal Eren, Ana Savić and Soley Ersoy ()
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Vladimir Baltić: School of Electrical and Computer Engineering, Academy of Technical and Art Applied Studies, 11000 Belgrade, Serbia
Kemal Eren: Sakarya University Technology Developing Zones Manager Company, 54050 Sakarya, Turkey
Ana Savić: School of Electrical and Computer Engineering, Academy of Technical and Art Applied Studies, 11000 Belgrade, Serbia
Soley Ersoy: Department of Mathematics, Faculty of Sciences, University of Sakarya, 54050 Sakarya, Turkey

Mathematics, 2024, vol. 12, issue 12, 1-16

Abstract: In this study, constant angle ruled surfaces with a pointwise 1-type Gauss map, which is very useful in the classification of surfaces, are investigated in terms of the Frenet elements of the base curves of the ruled surfaces in Euclidean 3-space. In order to form a basis for our work, firstly, basic concepts related to the Gauss map of an oriented surface are given. Later, a classification is satisfied by determining the necessary conditions to be the first kind, the second kind, and the harmonic of the pointwise 1-type of the Gauss map for these surfaces. Finally, some examples of these surfaces are provided, and their graphical illustrations are displayed.

Keywords: constant angle ruled surface; Gauss map; Laplace operator; pointwise 1-type map (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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