Riemannian manifolds of nullity index zero and curvature tensor-preserving transformations

Shûkichi TANNO

doi:10.2969/jmsj/02620258

Shûkichi TANNO

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JOURNAL FREE ACCESS

1974 Volume 26 Issue 2 Pages 258-271

DOI https://doi.org/10.2969/jmsj/02620258

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Published: 1974 Received: October 27, 1972 Available on J-STAGE: September 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 29, 2006 Reason for correction: - Correction: DTRECEIVED Details: Wrong : 19721002
Right : 19721027

Date of correction: September 29, 2006 Reason for correction: - Correction: TITLE Details: Wrong : Riemannian manifolds of nullity index zero and
Right : Riemannian manifolds of nullity index zero and curvature tensor-preserving transformations

Date of correction: September 29, 2006 Reason for correction: - Correction: SUBTITLE Details: Wrong : Dedicated to manifolds of nullity index zero and tensor-preserving transformations Professor S. Sasaki on his 60th birthday

Date of correction: September 29, 2006 Reason for correction: - Correction: AFFILIATION Details: Wrong :
1) Mathematical Institute Tohoku University

Right :
1) Mathematical Institute Tôhoku University

Date of correction: September 29, 2006 Reason for correction: - Correction: CITATION Details: Right : [1] S. S. Chern and N. H. Kuiper, Some theorems on the isometric imbedding of compact Riemann manifolds in euclidean space, Ann, of Math., 56 (1952), 422-430.
[2] S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, 1962.
[3] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, I, II, Intersci. Publ., 1963, 1969.
[4] O. Kowalski, On regular curvature structures, Math. Z., 125 (1972), 129-138.
[5] O. Kowalski, A note on the Riemann curvature tensor, Commentat. Math. Univ. Carolinae, 13 (1972), 257-263.
[6] M. Kurita, On the holonomy group of the conformally flat Riemannian manifold, Nagoya Math. J., 9 (1955), 161-171.
[7] K. Nomizu and K. Yano, Some results related to the equivalence problem in Riemannian geometry, Proc. U. S. -Japan Seminar in Differential Geometry, Kyoto, 1965, 95-100.
[8] A. Rosenthal, Riemannian manifolds of constant nullity, Michigan Math. J., 14 (1967), 469-480.
[9] P. J. Ryan, Homogeneity and some curvature conditions for hypersurfaces, Tôhoku Math. J., 22 (1969), 363-388.
[10] K. Sekigawa, On 4-dimensional connected Einstein space satisfying the condition R(X,Y)·R=0, Sci. Rep. Niigata Univ., 7 (1969), 29-31.
[11] K. Sekigawa, Notes on some 3- and 4-dimensional Riemannian manifolds, to appear.
[12] I. M. Singer, Infinitesimally homogeneous spaces, Comm. Pure Appl. Math., 13 (1960), 685-697.
[13] H. Takagi, An example of Riemannian manifolds satisfying R(X, Y)·R=0 but not ∇R=0, Tôhoku Math. J., 24 (1972), 105-108.
[14] H. Takagi and Y. Watanabe, On the holonomy groups of Kählerian manifolds with vanishing Bochner curvature tensor, Tôhoku Math. J., 25 (1973), 185-195.
[16] S. Tanno, Strongly curvature-preserving transformations of pseudo-Riemannian manifolds, Tôhoku Math. J., 19 (1967), 245-250.
[17] S. Tanno, Transformations of pseudo-Riemannian manifolds, J. Math. Soc. Japan, 21 (1969), 270-281.
[18] G. Vranceanu, Sur la représentation géodésique des espaces de Riemann, Rev. Roumaine Math. Pures Appl., 1, no. 3 (1956), 147-165.

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