Quantum mechanics

Ruled surface

Curvature

Ecology

Pure mathematics

Biology

Developable surface

Tangent

Operating system

Computer science

Frenet–Serret formulas

Gauss map

Surface (topology)

Type (biology)

Physics

Mathematics

Pointwise

Mathematical analysis

Gauss

Geometry

Euclidean space

Euclidean geometry

Space (punctuation)

Base (topology)

AIMS Mathematics

&lt;abstract&gt;&lt;p&gt;In this study, the ruled developable surfaces with pointwise 1-type Gauss map of Frenet-type framed base (Ftfb) curve are introduced in Euclidean 3-space. The tangent developable surfaces, focal developable surfaces, and rectifying developable surfaces with singular points are considered. Then the conditions for the Gauss map of these surfaces to be pointwise 1-type are obtained separately. In order to form a basis for the study, first, the basic concepts related to the Ftfb curve and the Gauss map of a surface are recalled. Later, the necessary and sufficient conditions are found for these surfaces to be of the pointwise 1-type of the Gauss map. Finally, examples for each type of these surfaces are given, and their graphics are illustrated.&lt;/p&gt;&lt;/abstract&gt;

The developable surfaces with pointwise 1-type Gauss map of Frenet type framed base curves in Euclidean 3-space