Geometric applications of critical point theory to submanifolds of complex projective space
- 1 November 1974
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 55, 5-31
- https://doi.org/10.1017/s0027763000016202
Abstract
In a recent paper, [6], Nomizu and Rodriguez found a geometric characterization of umbilical submanifolds Mn ⊂ Rn+p in terms of the critical point behavior of a certain class of functions Lp, p ⊂ Rn+p, on Mn. In that case, if p ⊂ Rn+p, x ⊂ Mn, then Lp(x) = (d(x,p))2, where d is the Euclidean distance function.Keywords
This publication has 4 references indexed in Scilit:
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- Reduction of the codimension of an isometric immersionJournal of Differential Geometry, 1971
- Differential geometry of complex hypersurfaces II*Journal of the Mathematical Society of Japan, 1968
- Differential Geometry of Complex HypersurfacesAnnals of Mathematics, 1967