The maximum number of linearly independent Killing vectors in an n-dimensional Riemannian manifold is established as n/2(n+1). This conclusion is derived from analyzing the second derivative of Killing vectors, where the first derivative is constrained to be antisymmetric. Specifically, for n space dimensions, the possible values of the Killing vector ξ are n, while the antisymmetrized first derivative yields n(n-1)/2. Thus, the total number of Killing vectors is calculated as n(n+1)/2.
PREREQUISITESThis discussion is beneficial for mathematicians, physicists, and students specializing in differential geometry, particularly those interested in the properties of Riemannian manifolds and their symmetries.