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Invariants of Time-like Curves in Lorentzian Spacetime
Wei LI
School of Mathematical Sciences, Capital Normal University, Beijing 100048
*Correspondence author
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Funding: Partially supported by SRFDP （No.20101108120001）
Opened online: 6 March 2014
Accepted by: none
Citation: Wei LI .Invariants of Time-like Curves in Lorentzian Spacetime[OL]. [ 6 March 2014] http://en.paper.edu.cn/en_releasepaper/content/4587044
 
 
This paper derives a family of invariants for time-like curves directly from the equation of its moving frames in Lorentzian spacetime. By the invariants this paper studies some geometric aspects of time-like curves in Lorentzian spacetime. In order to illustrate the necessity of constructing these invariants, this paper firstly reviews the traditional method with Frenet frame. Then one easily gets to find that for extending scope of application, it is necessary to discuss how to describe geometrical properties of curves with general orthonormal frames. A natural idea is to construct a family of invariants corresponding to orthonormal frames. These new invariants not only extend the traditional ones corresponding to Frenet frames, but also have better operability.
Keywords:pure mathematics; invariant; time-like curve; Lorentz spacetime; orthonormal frames
 
 
 

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