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The null curves on 3-null cone have the applications in the studying of horizon types. Via the pseudo-scalar product and Frenet equations, the differential geometry of null curves on 3-null cone is obtained. In the local sense, the curvature describes the contact of submanifolds with pseudo-spheres. We introduce the geometric properties of the null curves on 3-null cone and unit semi-Euclidean 3-spheres, respectively. On the other hand, we give the existence conditions of null Bertrand curves on 3-null cone and unit semi-Euclidean 3-spheres. c ⃝2015 All rights reserved.

Some new properties of null curves on 3-null cone and unit semi-Euclidean 3-spheres