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ON THE CONSTRUCTION OF PSEUDO-FINSLER EIKONAL EQUATIONS
( Muradiye Çimdiker ),( Cumali Ekici ) 호남수학회 2020 호남수학학술지 Vol.42 No.1
In this study, we have generalized pseudo-Finsler map by introducing the concept of semi-Riemannian map and have found pseudo-Finsler eikonal equations using pseudo-Finsler map. After that, we have obtained some sufficient theorems on pseudo-Finsler manifolds for the existence of solutions to the eikonal equation. At the same time, we have introduced a natural definition for the affine maps between pseudo-Finsler manifolds and have reached the affine solutions of them.
A NEW MODELLING OF TIMELIKE Q-HELICES
( Yasin Ünlütürk ),( Cumali Ekici ),( Doǧan Ünal ) 호남수학회 2023 호남수학학술지 Vol.45 No.2
In this study, we mean that timelike q-helices are curves whose q-frame fields make a constant angle with a non-zero fixed axis. We present the necessary and sufficient conditions for timelike curves via the q-frame to be q-helices in Lorentz-Minkowski 3-space. Then we find some results of the relations between q-helices and Darboux q-helices. Furthermore, we portray Darboux q-helices as special curves whose Darboux vector makes a constant angle with a non-zero fixed axis by choosing the curve as one of the types of q-helices, and also the general case.
( Yasin Unluturk ),( Suha Yilmaz ),( Cumali Ekici ) 호남수학회 2019 호남수학학술지 Vol.41 No.1
In this work, we study the conditions between null geodesic curves and timelike ruled surfaces in dual Lorentzian space. For this study, we establish a system of differential equations characterizing timelike ruled surfaces in dual Lorentzian space by using the invariant quantities of null geodesic curves on the given ruled surfaces. We obtain the solutions of these systems for special cases. Regarding to these special solutions, we give some results of the relations between null geodesic curves and timelike ruled surfaces in dual Lorentzian space.
Unluturk, Yasin,Yilmaz, Suha,Ekici, Cumali The Honam Mathematical Society 2019 호남수학학술지 Vol.41 No.1
In this work, we study the conditions between null geodesic curves and timelike ruled surfaces in dual Lorentzian space. For this study, we establish a system of differential equations characterizing timelike ruled surfaces in dual Lorentzian space by using the invariant quantities of null geodesic curves on the given ruled surfaces. We obtain the solutions of these systems for special cases. Regarding to these special solutions, we give some results of the relations between null geodesic curves and timelike ruled surfaces in dual Lorentzian space.
Yasin \"{U}nl\"{u}t\"{u}rk,S\"{u}ha Y\i lmaz,Cumali Ekici 호남수학회 2019 호남수학학술지 Vol.41 No.1
In this work, we study the conditions between null geodesic curves and timelike ruled surfaces in dual Lorentzian space. For this study, we establish a system of differential equations characterizing timelike ruled surfaces in dual Lorentzian space by using the invariant quantities of null geodesic curves on the given ruled surfaces. We obtain the solutions of these systems for special cases. Regarding to these special solutions, we give some results of the relations between null geodesic curves and timelike ruled surfaces in dual Lorentzian space.