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QUATERNIONS AND HOMOTHETIC MOTIONS IN EUCLIDEAN AND LORENTZIAN SPACES
( Gülsüm Yüca ),( Yusuf Yayli ) 호남수학회 2023 호남수학학술지 Vol.45 No.2
In the present paper, we investigate homothetic motions determined by quaternions, which is a general form of our previous paper [20]. We introduce a transition between homothetic motions in 3D and 4D Euclidean and Lorentzian spaces. In other words, we give a new method that works as a handy tool for obtaining Lorentzian homothetic motions from Euclidean homothetic motions. Moreover, some remarkable properties of homothetic motions, which are given in former studies on this subject, are also examined by dual transformations. Then, we present applications and visualize them with 3D-plots. Finally, we investigate homothetic motions in dual spaces because of the importance in many fields related to kinematics.
SOME RESULTS ON INVARIANT SUBMANIFOLDS OF AN ALMOST KENMOTSU (κ, μ, ν)-SPACE
( Mehmet Atçeken ),( Gülsüm Yüca ) 호남수학회 2021 호남수학학술지 Vol.43 No.4
In the present paper, we study the geometric properties of the invariant submanifold of an almost Kenmotsu structure whose Riemannian curvature tensor has (κ, μ, ν)-nullity distribution. In this connection, the necessary and sufficient conditions are investigated for an invariant submanifold of an almost Kenmotsu (κ, μ, ν)-space to be totally geodesic under the behavior of functions κ, μ, and ν.