Published: 1959 Received: August 15, 1957Available on J-STAGE: August 29, 2006Accepted: -
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Date of correction: August 29, 2006Reason for correction: -Correction: CITATIONDetails: Right : [1] L. Berwald, Untersuchung der Krümmung allgemeiner metrischer Räume auf Grund des in ihnen herrschenden Parallelismus. Math. Z., 25 (1926), 40-73. [2] L. Berwald, Über Finslersche und Cartansche Geometrie, II. Invarianten bei der Variation vielfacher Integrale und Parallelhyperflächen in Cartanschen Räumen Compositio Math., 7 (1940), 141-176. [3] S. S. Chern, Topics in Differential Geometry. Inst. for Advanced Study, Princeton, 1951. [4] E. Cartan, Les espaces métriques fondés sur la notion d'aire. Actual. Sci. Ind., No. 72, Hermann, Paris, 1933. [5] E. Cartan, Les espaces de Finsler. Actual. Sci. Ind., No. 79, Hermann, Paris, 1934. [6] E. T. Davies, Lie derivation in generalized metric spaces. Annali di Mat., ser. VI, 18 (1939), 261-274. [7] C. Ehresmann, Les connexions infinitésimales dans un espace fibré différentiable. Coll. De Topologie (Espaces Fibrés), C. B. R. M., Bruxelles, 29-55, 1951. [8] L. P. Eisenhart, Continuous groups of Transformations. Princeton Univ. Press, Princeton, 1933. [9] H. Hiramatsu, On affine collineations in a spaces of hyperplanes, Kumamoto J. Sci., 1 (1952), 1-7. [10] H. Hiramatsu, On projective collineations in a space of hyperplanes. Tensor, N. S., 2 (1952), 1-14. [11] H. Hiramatsu, Groups of homothetic transformations in a Finsler space. Tensor, N. S., 3 (1954), 131-143. [12] H. Hiramatsu, On some properties of groups of homothetic transformations in Riemannian and Finslerian spaces. Tensor, N. S., 4 (1954), 28-29. [13] S. Hokari, Winkeltreue Transformationen und Bewegungen im Finslerschen Raume. J. Fac. Sci. Hokkaido Imp. Univ., 5 (1936), 1-8. [14] S. Ishihara and T. Fukami, Groups of affine transformations and groups of projective transformations in a space of K-spreads. Japan. J. Math., 26 (1956), 79-93. [15] M. S. Knebelmann, Motions and collineations in general space. Proc. Nat. Acad. Sci. U. S. A., 13 (1927), 607-611. [16] M. S. Knebelmann, Collineations and motions in generalized spaces. Amer. J. Math. 51 (1929), 527-564. [17] S. Kobayashi, Groupe de transformations qui laissent invariante une connexion infinitésimale. C. R. Acad. Sci., Paris, 238 (1954), 644-645. [18] S. Kobayashi, Le groupe des transformations qui laissent invariant le parallélisme. Coll. De Topologie, Strasbourg, 1954. [20] D. Montgomery and H. Samelson, Transformation groups of spheres. Ann. of Math., 44 (1943), 454-470. [21] S. B. Myers and N. E. Steenrod, The group of isometries of a Riemann manifold. Ann. of Math., 40 (1939), 400-416. [22] A. Nijenhuis, The Theory of the Geometric Object. Proefschrift, Amsterdam, 1952. [23] K. Nomizu, On the group of affine transformations of an affinely connected manifold. Proc. Amer. Math. Soc., 4 (1953), 816-823. [24] K. Nomizu, Lie Groups and Differential Geometry. Publ. Math. Soc. Japan, No, 2, Tokyo, 1956. [25] T. Okubo, On the order of the groups of affine collineations in the generalized spaces of paths, I, II, III. Tensor, N. S., 6 (1956), 141-158; 7 (1957), 1-17, 18-33. [26] T. Otsuki, Theory of affine connections of the space of tangent directions of a differentiable manifold, I, II. Math. J. Okayama Univ., 7 (1957), 1-74. [27] J. A. Schouten, Ricci Calculus, 2nd. ed. Springer, Berlin, 1954. [28] N. E. Steenrod, The Topology of Fibre Bundles. Princeton Math. Ser., No. 14, Princeton, 1951. [29] Y. Tashiro, Sur la dérivée de Lie de l'être géométrique et son groupe d'invariance. Tôhoku Math. J., N. S., 2 (1950), 166-181. [30] Y. Tashiro, Note sur la dérivée de Lie d'un etre géométrique. Math. J. Okayama Univ., 1 (1952), 125-128. [31] Y. Tashiro, On universal tensorial forms on a principal fibre bundle. J. Math. Soc. Japan, 8 (1956), 247-255. [32] H. C. Wang, On Finsler spaces with completely integrable equations of Killing. J. London Math. Soc., 22 (1947), 5-9. [33] K. Yano, Lie derivatives in general space of paths. Proc. Japan Acad., 21 (1945), 363-371. [34] K. Yano, Groups of Transformations in Generalized Spaces. Akademia Press, Tokyo, 1949. [35] K. Yano, On n-dimensional Riemannian spaces admitting a group of motions of order n(n-1)/2+1. Trans. Amer. Math. Soc., 74 (1953), 260-279. [36] K. Yano, The Theory of Lie Derivatives and its Applications. Bibliotheca Math., vol. 3, North-Holland Publ. Co., Amsterdam, 1957. [37] K. Yano and H. Hiramatsu, Affine and projective geometries of system of hypersurfaces. J. Math. Soc. Japan, 3 (1951), 116-136. [38] K. Yano and H. Hiramatsu, On projective geometry of K-spreads. Compositio Math., 10 (1952), 286-296. [39] K. Yano and H. Hiramatsu, On groups of projective collineations in a space of K-spreads. J. Math. Soc. Japan, 6 (1954), 131-150.
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