^{page 78 note 1} This is the usual notation for covariant derivatives. With this notation, we could write r,_i for r_i.Google Scholar

^{page 78 note 2} Eisenhart, Riemannian Geometry, § 47. The notation used by Eisenhart will be used throughout the paper.

^{page 80 note 1} Quart. Journ. of Maths., 50 (1927), 277.Google Scholar

^{page 80 note 2} CfEisenhart, , loc. cit., p. 169.Google Scholar

^{page 82 note 1} We need not take tangent to V _n, but we do so to define the particular normal N'. All we actually know is that is orthogonal to N, and satisfies · r_i + N · S_i = 0.

^{page 83 note 1} An account of the principal directions of a tensor is given by Eisenhart, , loe. cit. § 33.Google Scholar

^{page 85 note 1} Trans. of the Amer. Math. Soc., 25 (1923), 297.CrossRefGoogle Scholar

^{page 85 note 2} Annals of Math., 27 (1926), 91.Google Scholar

^{page 86 note 1} Annali di Mat., 6 (1928–1929), 207.Google Scholar