Abstract
In this work, the embankment surfaces with pseudo null base curves are investigated in Minkowski 3-space. The representation formula of pseudo null curves is obtained via the defined structure functions and the k-type pseudo null helices are discussed completely. Based on the theories of pseudo null curves, a class of embankment surfaces are constructed and characterized by the structure functions of the pseudo null base curves.
Highlights
With the development of the theory of relativity, geometers and researchers often extend some topics in classical differential geometry of Riemannian manifolds to those of semi-Riemannian manifolds, especially to Lorentz–Minkowski manifolds
Due to the causal character of vectors in Lorentz–Minkowski space, some problems become a little strange and different, especially the ones related to lightlike vectors, such as null curves, pseudo null curves, B-scrolls and the marginally trapped surfaces and so on
Substituting the conclusions obtained in Corollary 3 to the representation formula shown by Proposition 2, after direct integrations, we have
Summary
With the development of the theory of relativity, geometers and researchers often extend some topics in classical differential geometry of Riemannian manifolds to those of semi-Riemannian manifolds, especially to Lorentz–Minkowski manifolds. The helix and the slant helix play important roles in the curve theory, and they can be applied into the science of biology and physics etc., such as analyzing the structure of DNA and characterizing the motion of particles in a magnetic field [2]. Due to these fascinating applications, the helix and the slant helix have been discussed widely, in the Euclidean space, and in the Lorentz–Minkowski space [3,4].
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