Complete Riemannian manifolds and some vector fields

Complete Riemannian manifolds and some vector fields
HTML articles powered by AMS MathViewer

by Yoshihiro Tashiro PDF

Trans. Amer. Math. Soc. 117 (1965), 251-275 Request permission

References

Georges de Rham, Sur la reductibilité d’un espace de Riemann, Comment. Math. Helv. 26 (1952), 328–344 (French). MR 52177, DOI 10.1007/BF02564308
Luthur Pfahler Eisenhart, An Introduction to Differential Geometry, Princeton Mathematical Series, vol. 3, Princeton University Press, Princeton, N. J., 1940. MR 0003048
S. I. Goldberg, Groups of transformations of Kaehler and almost Kaehler manifolds, Comment. Math. Helv. 35 (1961), 35–46. MR 123278, DOI 10.1007/BF02567003
Shigeru Ishihara and Yoshihiro Tashiro, On Riemannian manifolds admitting a concircular transformation, Math. J. Okayama Univ. 9 (1959/60), 19–47. MR 120588
Shigeru Ishihara, On infinitesimal concircular transformations, K\B{o}dai Math. Sem. Rep. 12 (1960), 45–56. MR 121744
Shoshichi Kobayashi, A theorem on the affine transformation group of a Riemannian manifold, Nagoya Math. J. 9 (1955), 39–41. MR 76395, DOI 10.1017/S0027763000023266

Some problems on transformations of Riemannian and Kählerian manifolds

Toshiyuki Maebashi, Vector fields and space forms, J. Fac. Sci. Hokkaido Univ. Ser. I 15 (1960), 62–92 (1960). MR 0140073
Albert Nijenhuis, On the holonomy groups of linear connections. IA, IB. General properties of affine connections, Nederl. Akad. Wetensch. Proc. Ser. A. 56 = Indagationes Math. 15 (1953), 233–240, 241–249. MR 0063737
Katsumi Nomizu, Lie groups and differential geometry, Mathematical Society of Japan, Tokyo, 1956. MR 0084166
Shigeo Sasaki and Morikuni Goto, Some theorems on holonomy groups of Riemannian manifolds, Trans. Amer. Math. Soc. 80 (1955), 148–158. MR 74872, DOI 10.1090/S0002-9947-1955-0074872-4
J. A. Schouten, Der Ricci-Kalkül, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 10, Springer-Verlag, Berlin-New York, 1978 (German). Eine Einführung in die neueren Methoden und Probleme der mehrdimensionalen Differentialgeometrie; Reprint of the 1924 original. MR 516659
Shun-ichi Tachibana, Some theorems on locally Riemannian spaces, Tohoku Math. J. (2) 12 (1960), 281–292. MR 157335, DOI 10.2748/tmj/1178244441
Yoshihiro Tashiro, On projective transformations of Riemannian manifolds, J. Math. Soc. Japan 11 (1959), 196–204. MR 123274, DOI 10.2969/jmsj/01130196
Yoshihiro Tashiro, Remarks on a theorem concerning conformal transformations, Proc. Japan Acad. 35 (1959), 421–422. MR 120589

On conformal collineations

10

Concircular geometry

16

18

Kentaro Yano, Kazuo Takano, and Yasuro Tomonaga, On infinitesimal deformations of curves in spaces with linear connection, Jpn. J. Math. 19 (1948), 433–477. MR 35083
Kentaro Yano, The theory of Lie derivatives and its applications, North-Holland Publishing Co., Amsterdam; P. Noordhoff Ltd., Groningen; Interscience Publishers Inc., New York, 1957. MR 0088769
Kentaro Yano and Tadashi Nagano, Einstein spaces admitting a one-parameter group of conformal transformations, Ann. of Math. (2) 69 (1959), 451–461. MR 101535, DOI 10.2307/1970193
Kentaro Yano and Tadashi Nagano, The de Rham decomposition, isometries and affine transformations in Riemannian spaces, Jpn. J. Math. 29 (1959), 173–184. MR 120591, DOI 10.4099/jjm1924.29.0_{1}73