Generalized Spacelike Normal Curves in Minkowski Three-Space

Equiform geometry is considered an extension of other geometries. Furthermore, an equiform frame is a generalization of the Frenet frame. In this study, we begin by defining the term “equiform parameter (EQP)”, “equiform frame”, and “equiform formulas (EQF)” in regard to the Minkowski three-space. S...

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Published inMathematics (Basel) Vol. 10; no. 21; p. 4145
Main Authors Tashkandy, Yusra, Emam, Walid, Cesarano, Clemente, Abd El-Raouf, M. M., Elsharkawy, Ayman
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.11.2022
Subjects
Analysis
Curves
equiform curvatures
equiform equations
equiform frame
equiform normal curves
Euclidean space
Gaussian distribution
Geometry
Mathematicians
Minkowski three-space
Space and time
Egypt
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Abstract Equiform geometry is considered an extension of other geometries. Furthermore, an equiform frame is a generalization of the Frenet frame. In this study, we begin by defining the term “equiform parameter (EQP)”, “equiform frame”, and “equiform formulas (EQF)” in regard to the Minkowski three-space. Second, we define spacelike normal curves (SPN) in Minkowski three-space and present a variety of descriptions of these curves with equiform spacelike (EQS) or equiform timelike (EQN) principal normals in Minkowski three-space. Third, we discuss the implications of these findings. Finally, an example is given to illustrate our theoretical results.
AbstractList Equiform geometry is considered an extension of other geometries. Furthermore, an equiform frame is a generalization of the Frenet frame. In this study, we begin by defining the term “equiform parameter (EQP)”, “equiform frame”, and “equiform formulas (EQF)” in regard to the Minkowski three-space. Second, we define spacelike normal curves (SPN) in Minkowski three-space and present a variety of descriptions of these curves with equiform spacelike (EQS) or equiform timelike (EQN) principal normals in Minkowski three-space. Third, we discuss the implications of these findings. Finally, an example is given to illustrate our theoretical results.
Audience Academic
Author Tashkandy, Yusra
Emam, Walid
Elsharkawy, Ayman
Cesarano, Clemente
Abd El-Raouf, M. M.
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Cites_doi 10.1007/s00022-013-0205-z
10.1002/mma.4618
10.1155/2014/402360
10.1186/s42787-020-00086-4
10.1155/2013/651495
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SubjectTerms Analysis
Curves
equiform curvatures
equiform equations
equiform frame
equiform normal curves
Euclidean space
Gaussian distribution
Geometry
Mathematicians
Minkowski three-space
Space and time
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