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Based on an examination of the solutions to the Killing Vector equations forthe FLRW-metric in co moving coordinates , it is conjectured and proved thatthe components(in these coordinates) of Killing Vectors, when suitably scaledby functions, are \emph{zero modes} of the corresponding \emph{scalar}Laplacian. The complete such set of zero modes(infinitely many) are explicitlyconstructed for the two-sphere. They are parametrised by an integer n. For$n\,\ge\,2$, all the solutions are \emph{irregular} (in the sense that they areneither well defined everywhere nor are \emph{square-integrable}). Theassociated 2-d vectors are also \emph{not normalisable}. The $n=0$ solutionsbeing constants (these correspond to the zero angular momentum solutions) areregular and normalizable. Not all of the $n=1$ solutions are regular but theassociated vectors are normalizable. Of course, the action of scalar Laplaciancoordinate independent significance only when acting on scalars. However, ourconclusions have an unambiguous meaning as long as one works in this coordinatesystem. As an intermediate step, the covariant Laplacians(vector Laplacians) ofKilling vectors are worked out for four-manifolds in two different ways, bothof which have the novelty of not explicitly needing the connections. It isfurther shown that for certain maximally symmetric sub-manifolds(hypersurfacesof one or more constant comoving coordinates) of the FLRW-spaces also, thescaled Killing vector components are zero modes of their corresponding scalarLaplacians. The Killing vectors for the maximally symmetric four-manifolds areworked out using the elegant embedding formalism originally due toSchr\"odinger . Some consequences of our results are worked out. Relevance tosome very recent works on zero modes in AdS/CFT correspondences , as well as onbraneworld scenarios is briefly commented upon.

Killing vectors of FLRW metric (in comoving coordinates) and zero modes of the scalar Laplacian