Some differential equations on Riemannian manifolds

Shûkichi TANNO

doi:10.2969/jmsj/03030509

Shûkichi TANNO

著者情報

ジャーナルフリー

1978 年 30 巻 3 号 p. 509-531

DOI https://doi.org/10.2969/jmsj/03030509

詳細

Published: 1978 Received: 1977/03/26 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 著者情報訂正内容: Wrong : Shukichi TANNO¹⁾
Right : Shûkichi TANNO¹⁾

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 所属機関情報訂正内容: 訂正前 :
1) Mathematical Institute Tohoku University

訂正後 :
1) Mathematical Institute Tôhoku University

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: 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.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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