On principal normal vector fields of submanifolds in a Riemannian manifold of constant curvature

Tominosuke OTSUKI

doi:10.2969/jmsj/02210035

Tominosuke OTSUKI

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JOURNAL FREE ACCESS

1970 Volume 22 Issue 1 Pages 35-46

DOI https://doi.org/10.2969/jmsj/02210035

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Published: 1970 Received: March 27, 1969 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: AUTHOR Details: Wrong : Tominosuke OTSUKI¹⁾
Right : Tominosuke OTSUKI¹⁾²⁾

Date of correction: September 29, 2006 Reason for correction: - Correction: AFFILIATION Details: Wrong :
1) University of California, Berkeley Tokyo Institute fo Technology

Right :
1) University of California
2) Tokyo Institute of Technology

Date of correction: September 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) S.S. Chern, M. DoCarmo and S. Kobayashi, Minimal submanifolds of a sphere with second fundamental form of constant length, to appear.
2) R. Maltz, Isometric immersion into spaces of constant curvature, to appear.
3) B. O'Neill, Isometric immersions which preserve curvature operators, Proc. Amer. Math. Soc., 13 (1962), 759-763.
4) B. O'Neill, Isometric immersion of flat Riemannian manifolds in Euclidean space, Michigan Math. J., 9 (1962), 199-205.
5) B. O'Neill, Umbilic of constant curvature immersions, Duke Math. J., 32 (1965), 149-159.
6) B. O'Neill and E. Stiel, Isometric immersions of constant curvature manifolds, Michigan Math. J., 10 (1963), 335-339.
7) T. Otsuki, A theory of Riemmanian submanifolds, Kodai Math. Sem. Rep., 20 (1968), 282-295.
8) T. Otsuki, Pseudo-umbilical submanifolds with M-index_??_1 in Euclidean spaces, Kodai Math. Sem. Rep., 20 (1968), 296-304.
9) T. Otsuki, Minimal hypersurfaces in a Riemannian manifold of constant curvature, to appear.
10) E. Stiel, Isometric immersions of manifolds of nonnegative constant sectional curvature, Pacific J. Math., 15 (1965), 1415-1419.

Right : [1] S. S. Chern, M. DoCarmo and S. Kobayashi, Minimal submanifolds of a sphere with second fundamental form of constant length, to appear.
[2] R. Maltz, Isometric immersion into spaces of constant curvature, to appear.
[3] B. O'Neill, Isometric immersions which preserve curvature operators, Proc. Amer. Math. Soc., 13 (1962), 759-763.
[4] B. O'Neill, Isometric immersion of flat Riemannian manifolds in Euclidean space, Michigan Math. J., 9 (1962), 199-205.
[5] B. O'Neill, Umbilic of constant curvature immersions, Duke Math. J., 32 (1965), 149-159.
[6] B. O'Neill and E. Stiel, Isometric immersions of constant curvature manifolds, Michigan Math. J., 10 (1963), 335-339.
[7] T. Otsuki, A theory of Riemmanian submanifolds, Kodai Math. Sem. Rep., 20 (1968), 282-295.
[8] T. Otsuki, Pseudo-umbilical submanifolds with M-index≤1 in Euclidean spaces, Kodai Math. Sem. Rep., 20 (1968), 296-304.
[9] T. Otsuki, Minimal hypersurfaces in a Riemannian manifold of constant curvature, to appear.
[10] E. Stiel, Isometric immersions of manifolds of nonnegative constant sectional curvature, Pacific J. Math., 15 (1965), 1415-1419.

Date of correction: September 29, 2006 Reason for correction: - Correction: PDF FILE Details: -

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