@article{oai:teapot.lib.ocha.ac.jp:00034849,
 author = {Ogawa, Yosuke and Sekizawa, Masami},
 issue = {2},
 journal = {お茶の水女子大學自然科學報告},
 month = {Dec},
 note = {application/pdf, 紀要論文, In 1968, J. Simons [3] has established a formula for the Laplacian of the second fundamental form of a submanifold and has obtained some applications in the case of minimal hypersurfaces in the sphere. A formula of Simons' type has been improved by K. Nomizu and B. Smyth [2] in 1969. Based on the new formula of Simons' type, they have determined hypersurfaces of non-negative sectional curvature and constant mean curvature immersed in the Euclidean space or the sphere under the additional assumption which is satisfied if M is compact. In the present paper, we first obtain a formula of Simons' type (2.11) in the case of a hypersurface M immersed with constant mean curvature in a conformally flat Riemannian manifold M^^〜 which satisfies some additional assumptions. These assumptions are described in terms of the Ricci operator of M^^〜 and naturally satisfied if M^^〜 is a space of constant sectional curvature. _Our main results are the determination of the immersions of M into M^^〜 when M admits non-negative sectional curvature.},
 pages = {77--87},
 title = {Hypersurfaces Immersed in a Conformally Flat Riemannian Manifold : Dedicated to Professor S. Tachibana on his 50th Birthday},
 volume = {27},
 year = {1976}
}