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In this paper, we use the Killing vector method to formulate the deSitter/Anti-de Sitter invariant special relativity (dS/AdS-SR). Through solvingthe Einstein equation with $\Lambda\neq 0$, the basic inertial metric fordS/AdS-SR is determined to be the Beltrami metric $B_{\mu\nu}(x)$. Thecorresponding Killing equations are system of ten simultaneous partialdifferential equations of first order. Their most general solutions wereobtained, and all the ten independent Killing vectors were found out. Theseresults confirm that the Beltrami metric has maximal spacetime symmetry. Theten Killing-Noether charges are obtained. They are energy, momenta, Lorentzboost and angular momentum in SR-theory with $\Lambda\neq 0$. Consequently,dS/AdS-SR is consistently established for the vacuum with $\Lambda\neq 0$ viaKilling vector method rather than the unpopular classical domain theory.

Killing Vectors in Spacetime of the De Sitter Invariant Special Relativity