A certain property of geodesics of the family of Riemannian manifolds \(O^ 2_ n\). IX
This is a continuation of Part VIII [ibid. 9, 272-307 (1986; Zbl 0601.53041)] with the same title written by the present author which proved that the so-called conjecture C is true for 4.5\(\leq n\leq 5\). The method of proof given then for \(3\leq n\leq 5\) was not so effective, when n comes near 3 and we know that this method still does not work well for the proof of conjecture C for \(2\leq n\leq 3\) by Lemma 8.1 of Part III [ibid. 4, 28-70 (1981; Zbl 0469.53040)]. In the present paper we shall show that this conjecture is also true for 2.4\(\leq n\leq 4.5\) by a new method of proof.
scientific article; zbMATH DE number 4056480
scientific article