Published: 1978 Received: March 26, 1977Available on J-STAGE: October 20, 2006Accepted: -
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Date of correction: October 20, 2006Reason for correction: -Correction: AUTHORDetails: Wrong : Shukichi TANNO1) Right : Shûkichi TANNO1)
Date of correction: October 20, 2006Reason for correction: -Correction: AFFILIATIONDetails: Wrong :
1) Mathematical Institute Tohoku University
Right :
1) Mathematical Institute Tôhoku University
Date of correction: October 20, 2006Reason for correction: -Correction: CITATIONDetails: Wrong : 1) K. Abe, A characterization of totally geodesic submanifolds in Sn and CPn by an inequality, Tohoku Math. J., 23 (1971), 139-244. 2) M. Berger, P. Gauduchon and E. Mazet, Le spectre d'une variété riemannienne, Lecture Notes in Math., 194, Springer-Verlag. 3) D. E. Blair, On the characterization of complex projective space by differential equations, J. Math. Soc. Japan, 27 (1975), 9-19. 4) 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. 5) Y. H. Clifton and R. Maltz, The k-nullity space of curvature operator, Michigan Math. J., 17 (1970), 85-89. 6) D. Ferus, Totally geodesic foliations, Math. Ann., 188 (1970), 313-316. 7) D. Ferus, On the completeness of nullity foliations, Michigan Math. J., 18 (1971), 61-64. 8) D. Ferus, A characterization of Riemannian symmetric spaces of rank one, (preprint). 9) S. Gallot, Variétés dont le spectre ressemble à celui de la sphère, Compt. Rend. Acad. Paris, 283 (1976), 647-650. 10) A. Gray, Spaces of constancy of curvature operators, Proc. Amer. Math. Soc., 17 (1966), 897-902. 11) S. Ishihara and Y. Tashiro, On Riemannian manifolds admitting a concircular transformation, Math. J. Okayama Univ., 9 (1959), 19-47. 12) R. Maltz, The nullity spaces of curvature operator, Cahiers de Topologie et Géom. Diff., 8 (1966), 1-20. 13) T. Nagano, The projective transformation on a space with parallel Ricci tensor, Kodai Math. Sem. Rep., 11 (1959), 131-138. 14) M. Obata, Certain conditions for a Riemannian manifold to be isometric with a sphere, J. Math. Soc. Japan, 14 (1962), 333-340. 15) M. Obata, Riemannian manifolds admitting a solution of a certain system of differential equations, Proc. U. S.-Japan Sem. in Differential Geom., Kyoto, Japan, 1965, 101-114, 16) S. Tachibana, On infinitesimal holomorphically projective transformations in certain almost Hermitian spaces, Nat. Sci. Rep. Ochanomizu Univ., 10 (1959), 45-51. 17) S. Tachibana and W. N. Yu, On a Riemannian space admitting more than one Sasakian structure, Tohoku Math. J., 22 (1970), 536-540. 18) S. Tanno, On the isometry groups of Sasakian manifolds, J. Math. Soc. Japan, 22 (1970), 579-590. 19) S. Tanno, Killing vectors on contact Riemannian manifolds and fiberings related to the Hopf fibrations, Tohoku Math. J., 23 (1971), 313-333. 20) S. Tanno, Some system of differential equations on Riemannian manifolds and its applications to contact structures, Tohoku Math. J., 29 (1977), 125-136. 21) S. Tanno, Differential equations of order 3 on Riemannian manifolds, (technical report). 22) Y. Tashiro, Complete Riemannian manifolds and some vector fields, Trans. Amer. Math. Soc., 117 (1965), 251-275. 23) K. Yano, The theory of Lie derivatives and its applications, Amsterdam, 1957. 24) K. Yano, Differential geometry on complex and almost complex spaces, Pergamon Press, 1965.
Right : [1] K. Abe, A characterization of totally geodesic submanifolds in Sn and CPn by an inequality, Tôhoku Math. J., 23 (1971), 139-244. [2] M. Berger, P. Gauduchon and E. Mazet, Le spectre d'une variété riemannienne, Lecture Notes in Math., 194, Springer-Verlag. [3] D. E. Blair, On the characterization of complex projective space by differential equations, J. Math. Soc. Japan, 27 (1975), 9-19. [4] 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. [5] Y. H. Clifton and R. Maltz, The k-nullity space of curvature operator, Michigan Math. J., 17 (1970), 85-89. [6] D. Ferus, Totally geodesic foliations, Math. Ann., 188 (1970), 313-316. [7] D. Ferus, On the completeness of nullity foliations, Michigan Math. J., 18 (1971), 61-64. [8] D. Ferus, A characterization of Riemannian symmetric spaces of rank one, (preprint). [9] S. Gallot, Variétés dont le spectre ressemble à celui de la sphère, Compt. Rend. Acad. Paris, 283 (1976), 647-650. [10] A. Gray, Spaces of constancy of curvature operators, Proc. Amer. Math. Soc., 17 (1966), 897-902. [11] S. Ishihara and Y. Tashiro, On Riemannian manifolds admitting a concircular transformation, Math. J. Okayama Univ., 9 (1959), 19-47. [12] R. Maltz, The nullity spaces of curvature operator, Cahiers de Topologie et Géom. Diff., 8 (1966), 1-20. [13] T. Nagano, The projective transformation on a space with parallel Ricci tensor, Kodai Math. Sem. Rep., 11 (1959), 131-138. [14] M. Obata, Certain conditions for a Riemannian manifold to be isometric with a sphere, J. Math. Soc. Japan, 14 (1962), 333-340. [15] M. Obata, Riemannian manifolds admitting a solution of a certain system of differential equations, Proc. U. S.-Japan Sem. in Differential Geom., Kyoto, Japan, 1965, 101-114, [16] S. Tachibana, On infinitesimal holomorphically projective transformations in certain almost Hermitian spaces, Nat. Sci. Rep. Ochanomizu Univ., 10 (1959), 45-51. [17] S. Tachibana and W. N. Yu, On a Riemannian space admitting more than one Sasakian structure, Tôhoku Math. J., 22 (1970), 536-540. [18] S. Tanno, On the isometry groups of Sasakian manifolds, J. Math. Soc. Japan, 22 (1970), 579-590. [19] S. Tanno, Killing vectors on contact Riemannian manifolds and fiberings related to the Hopf fibrations, Tôhoku Math. J., 23 (1971), 313-333. [20] S. Tanno, Some system of differential equations on Riemannian manifolds and its applications to contact structures, Tôhoku Math. J., 29 (1977), 125-136. [21] S. Tanno, Differential equations of order 3 on Riemannian manifolds, (technical report). [22] Y. Tashiro, Complete Riemannian manifolds and some vector fields, Trans. Amer. Math. Soc., 117 (1965), 251-275. [23] K. Yano, The theory of Lie derivatives and its applications, Amsterdam, 1957. [24] K. Yano, Differential geometry on complex and almost complex spaces, Pergamon Press, 1965.
Date of correction: October 20, 2006Reason for correction: -Correction: PDF FILEDetails: -