Submanifolds of a Euclidean space with homothetic Gauss map

Yosio MUTO

doi:10.2969/jmsj/03230531

Yosio MUTO

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JOURNAL FREE ACCESS

1980 Volume 32 Issue 3 Pages 531-555

DOI https://doi.org/10.2969/jmsj/03230531

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Published: 1980 Received: October 23, 1978 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) M. P. do Carmo and N. R. Wallach, Minimal immersions of spheres into spheres, Ann. of Math., (2) 93 (1971), 43-62.
2) D. Ferus, Immersionen mit paralleler zweiter Fundamentalform: Beispiele und Nicht-Beispiele, Manuscripta Math., 12 (1974), 153-162.
3) D. Ferus, Immersions with parallel second fundamental form, Math. Z., 140 (1974), 87-93.
4) D. Ferus, Produkt-Zerlegung von Immersionen mit paralleler zweiter Fundamentalform, Math. Ann., 211 (1974), 1-5.
5) T. Itoh, On Veronese manifolds, J. Math. Soc. Japan, 27 (1975), 497-506.
6) T. Itoh and K. Ogiue, Isotropic immersions and Veronese manifolds, Trans. Amer. Math. Soc., 209 (1975), 109-117.
7) K. Leichtweiss, Zur Riemannschen Geometrie in Grassmannschen Mannigfaltigkeiten, Math. Z., 76 (1961), 334-366.
8) Y. Muto, The Gauss map of a submanifold in a Euclidean space, J. Math. Soc. Japan, 30 (1978), 85-100.
9) M. Obata, The Gauss map of immersions of Riemannian manifolds in spaces of constant curvature, J. Differential Geometry, 2 (1968), 217-223.
10) B. O'Neill, Isotropic and Kähler immersions, Canad. J. Math., 17 (1965), 907-915.
11) E. A. Ruh and J. Vilms, The tension field of the Gauss map, Trans. Amer. Math. Soc., 149 (1970), 569-573.
12) T. Takahashi, Minimal immersions of Riemannian manifolds, J. Math. Soc. Japan, 18 (1966), 380-385.
13) J. Vilms, Submanifolds of Euclidean space with parallel second fundamental form, Proc. Amer. Math. Soc., 32 (1972), 263-267.

Right : [1] M. P. do Carmo and N. R. Wallach, Minimal immersions of spheres into spheres, Ann. of Math., (2) 93 (1971), 43-62.
[2] D. Ferus, Immersionen mit paralleler zweiter Fundamentalform: Beispiele und Nicht-Beispiele, Manuscripta Math., 12 (1974), 153-162.
[3] D. Ferus, Immersions with parallel second fundamental form, Math. Z., 140 (1974), 87-93.
[4] D. Ferus, Produkt-Zerlegung von Immersionen mit paralleler zweiter Fundamentalform, Math. Ann., 211 (1974), 1-5.
[5] T. Itoh, On Veronese manifolds, J. Math. Soc. Japan, 27 (1975), 497-506.
[6] T. Itoh and K. Ogiue, Isotropic immersions and Veronese manifolds, Trans. Amer. Math. Soc., 209 (1975), 109-117.
[7] K. Leichtweiss, Zur Riemannschen Geometrie in Grassmannschen Mannigfaltigkeiten, Math. Z., 76 (1961), 334-366.
[8] Y. Muto, The Gauss map of a submanifold in a Euclidean space, J. Math. Soc. Japan, 30 (1978), 85-100.
[9] M. Obata, The Gauss map of immersions of Riemannian manifolds in spaces of constant curvature, J. Differential Geometry, 2 (1968), 217-223.
[10] B. O'Neill, Isotropic and Kähler immersions, Canad. J. Math., 17 (1965), 907-915.
[11] E. A. Ruh and J. Vilms, The tension field of the Gauss map, Trans. Amer. Math. Soc., 149 (1970), 569-573.
[12] T. Takahashi, Minimal immersions of Riemannian manifolds, J. Math. Soc. Japan, 18 (1966), 380-385.
[13] J. Vilms, Submanifolds of Euclidean space with parallel second fundamental form, Proc. Amer. Math. Soc., 32 (1972), 263-267.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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