×

A theory of extended Lie transformation groups. (English) Zbl 0134.39201


Full Text: DOI

References:

[1] Takasu, T., Erweiterung des Erlanger Programms durch Transformationsgruppenerweiterungen, Proc. Japan Acad., 34, 471-476 (1958) · Zbl 0100.15304 · doi:10.3792/pja/1195524555
[2] Takasu, T., Extended Euclidean Geometry and Extended Equiform Geometry under the Extensions of Respective Transformation Groups. I, Yokohama Math. J., 6, 89-177 (1958) · Zbl 0139.38802
[3] Takasu, T., Extended Euclidean Geometry and Extended Equiform Geometry under the Extensions of Respective Trasformation Groups. II, Yokohama Math. J., 7, 1-88 (1959) · Zbl 0136.43002
[4] Takasu, T., Extended Affine Geometry. I, Yokohama Math. J., 7, 154-185 (1959) · Zbl 0094.35103
[5] Takasu, T., Extended Non-Euclidean Geometry, Proc. Japan Acad., 36, 179-182 (1960) · Zbl 0100.35103 · doi:10.3792/pja/1195524049
[6] Takasu, T., Extended Non-Euclidean Geometry obtained by Extending the Group Parameters to Functions of Coordinates, Yokohama Math. J., 8, 1-58 (1960) · Zbl 0139.38803
[7] Takasu, T., Adjusted Relativity Theory: Applications of Extended Euclidean Geometry, Extended Equiform Geometry and Extended Laguerre Geometry to Physics, Yokohama Math. J., 7, 1-42 (1959) · Zbl 0127.43602
[8] Takasu, T., Extended Conformal Geometry obtained by Extending the Group Parameters to Functions of Coordinates. I, Yokohama Math. J., 8, 85-172 (1960) · Zbl 0139.38901
[9] Takasu, T., Extended Projective Geometry obtained by Extending the Group Parameters to Functions of Coordinates. I, Yokohama Math. J., 9, 29-84 (1961) · Zbl 0114.12602
[10] Takasu, T., Extended Lie Geometry, Extended Parabolic Lie Geometry, Extended Equiform Laguerre Geometry and Etended Laguerre Geometry and their Realizations in the Differentiable Manifolds, Yokohama Math. J., 9, 85-130 (1962) · Zbl 0116.14103
[11] – –,Extended Affine Principal Fibre Bundles. « Annali di Matematica Pura e Applicata. » Serie IV — Tomo-LIV-(1961), 85-97. · Zbl 0196.54203
[12] Sophus Lie —Georg Scheffers,Vorlesungen über continuirliche Gruppen mit geometrischen und anderen Anwendungen. « Leipzig, B. G. Teubner », (1893), 1-810. · JFM 25.0623.02
[13] Otto Schreier,Abstrakte kontinuirliche Grupprn. « Hamburger Abhandlungen », 4 (1926). · JFM 52.0166.02
[14] – –,Die Vewandschaft stetiger Gruppen im Grossen. « Hamburger Abhandlungen », 5 (1927).
[15] E. Cartan,La Géométrie des Groupes de Transformations. « Liouvilles Journal de Mathématiques pures ed appliqueés », VI, Fasc., (1927), 1-119. · JFM 53.0388.01
[16] L. Pontriagin,Topological groups (1939). · JFM 61.1217.01
[17] L. van der Waerden,Vorlesungen über kontinuirliche Gruppen, (1959).
[18] G. Birkhoff,Analytical groups. « Trans Amer. Math. Soc., 43 (1938). · Zbl 0018.20502
[19] P. A. Smith,Foundation of Lie Groups. « Ann. of. Math. », 48 (1947). · Zbl 0031.00702
[20] Andrè Lichnerowicz,Géométrie des Groupes de Transformations. Dunod Paris (1958). · Zbl 0096.16001
[21] Horie, N., On the holonomy group spaces, Memoirs of the College of Science, Univ. of Kyoto, Ser. A, XXVIII, 2, 161-167 (1953) · Zbl 0055.25702
[22] Horie, N., On some properties of trajectories of the group spaces, Memoirs of the College of Science», Univ. of Kyoto, Ser. A, XVIII, 2, 169-178 (1953) · Zbl 0055.25703
[23] Horie, N., On cyclic points of the group spaces, Memoirs of the College of Science, Univ. of Kyoto, Ser. A, XXIX, 1, 35-41 (1955) · Zbl 0065.01403
[24] – –,On the group-space of the continuous transformation group with a Riemannian metric. « Memoirs of the College of Science, Univ. of Kyoto », Math. N^o. 1 (1956) 23-42. · Zbl 0074.37703
[25] Ahn, J. K., On the parameter group manifold, Kyungpook Math. Jour., 2, 2, 39-45 (1959)
[26] Ahn, J. K., The Correspondences of the Fundamental Frames on the Parameter Group Manifolds, Kyunpook Math. Jour., 3, 1, 31-37 (1960)
[27] Bark, O. Y., The Infinitesimal Transformations in the Parameter Group Manifolds, Kyunpook Math Jour., 4, 1, 5-12 (1961)
[28] Bredon, G. E., Some theorems on transformation groups, Ann. of Math., 67, 104-118 (1958) · Zbl 0094.01601 · doi:10.2307/1969930
[29] Gleason, A. M., Spaces with a compact Lie group of transformations, Proc. Amer. Math. Soc., 1, 35-43 (1950) · Zbl 0041.36207 · doi:10.1090/S0002-9939-1950-0033830-7
[30] Montgomery, D.; Zippin, L., Topological Transformation Groups. I, Ann. of Math., 41, 778-791 (1040) · Zbl 0025.23701 · doi:10.2307/1968858
[31] – –,Topological Transformation Groups. Interscience Press (1955). · Zbl 0068.01904
[32] Karube, T., The local structure of an orbit of a transformation group, Proc. Jap. Acad., 37, 212-214 (1961) · Zbl 0133.16204 · doi:10.3792/pja/1195523742
[33] Karube, T., The Local Structure of an Orbit of a Transformation Group, Proc. Japan Acad., 37, 212-214 (1961) · Zbl 0133.16204 · doi:10.3792/pja/1195523742
[34] T. Takasu,Duality in the Linear Connections in the Large. « The Tensor » (1963) under press.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.