Abstract
In this paper, new vector fields are defined along a curve lying on an orientable hypersurface with nonvanishing extended Darboux curvatures of the second kind, and some new planes and curves are introduced using these vector fields in Euclidean 4-space. It is also shown that in 4-dimensional space, these new planes play the same role that the Darboux vector W = 𝜏𝑔T − 𝜅𝑛V + 𝜅𝑔N plays in Euclidean 3-space. Besides, developable and non-developable ruled hypersurfaces associated with these new vector fields are defined.
Keywords
Frame (networking)
Vector field
Pure mathematics
Physics
Algebra over a field
Geometry
Mathematics
Computer science
Telecommunications
Subject Areas
Elasticity and Wave Propagation
·Mechanics of Materials ·Physical Sciences
Differential Equations and Numerical Methods
·Numerical Analysis ·Physical Sciences
Numerical methods for differential equations
·Numerical Analysis ·Physical Sciences
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