Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Isotropic immersions and Veronese manifolds


Authors: T. Itoh and K. Ogiue
Journal: Trans. Amer. Math. Soc. 209 (1975), 109-117
MSC: Primary 53C40
DOI: https://doi.org/10.1090/S0002-9947-1975-0375172-8
MathSciNet review: 0375172
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: An $ n$-dimensional Veronese manifold is defined as a minimal immersion of an $ n$-sphere of curvature $ n/2(n + 1)$ into an $ \{ n(n + 3)/2 - 1\} $-dimensional unit sphere. The purpose of this paper is to give some characterizations of a Veronese manifold in terms of isotropic immersions.


References [Enhancements On Off] (What's this?)

  • [1] S. S. Chern, M. do Carmo and S. Kobayashi, Minimal submanifolds of a sphere with second fundamental form of constant length, Functional Analysis and Related Fields (Proc. Conf. for M. Stone, Univ. Chicago, Chicago, Ill., 1968), Springer, New York, 1970, pp. 59-75. MR 42 #8424. MR 0273546 (42:8424)
  • [2] M.P. do Carmo and N. R. Wallach, Minimal immersions of spheres into spheres, Ann. of Math. (2) 93 (1971), 43-62. MR 43 = 4048. MR 0278318 (43:4048)
  • [3] J. A. Erbacher, Reduction of the codimension of an isometric immersion, J. Differential Geometry 5 (1971), 333-340. MR 44 #5897. MR 0288701 (44:5897)
  • [4] T. Itoh and K. Ogiue, Isotropic immersions, J. Differential Geometry 8 (1973), 305-316. MR 0380682 (52:1579)
  • [5] B. O'Neill, Isotropic and Kähler immersions, Canad. J. Math. 17 (1965), 907-915. MR 32 #1654. MR 0184181 (32:1654)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 53C40

Retrieve articles in all journals with MSC: 53C40


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0375172-8
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society