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Statement of Theorem 3 contains some errors. Sentence "Another geodesic is closed geodesic of length 2π and of multiplicity 1." in the lines 23-24 and 28-29 on page 410 should be replaced by "All closed geodesies of length 2π/q are obtained as above. Other geodesies through these points are closed geodesies of length 2π (resp. π) in case of (i) (resp. (ii)) and of multiplicity 1." Nevertheless arguments in the lines 4-14 on page 410 are valid when q is a prime or cos (2πpjq) = = cos (2πpjq) holds. So Corollaries 1, 2 to Theorem 3 remain true. Thus Theorem 3 determines closed geodesies of length 2π/q. Now we shall determine all closed geodesies of lens spaces. Generally closed geodesies of a lens space of constant curvature 1 are of length 2πk/q(k = 1, 2, , q: if q is odd and k = 1, 2, , q/2: if q is (k) even). First let us introduce the equivalence relation ~ in {plf — -,pn}. Let Si (i = 1, , n) be an integer such that 8tpt = k(moaq). Note that Si is determined modulo q. Then we define pt ~ p3if and only if cos (2πpiSj/q) = cos (2πk/q). As is easily seen, this is an equivalence relation. Let {p, = ph, , p,-m; Psmb+i+l9 , P;m& = Psn] be a partition of {pu ---,Pn} with respect to this equivalence relation. Now a point p = φ(χu •••,»») is said to be —adapted if there exists an s e {mu , mh) and x2j^ = x23= 0 holds for ps e {pu . , pn} {Pjna_i+ί, , Vim). Now we have

Correction and supplement to: ``On closed geodesics of lens spaces''