Given an immersed submanifold $M^n\subset\mathbb{R}^{n+2}$, we characterize
the vanishing of the normal curvature $R_D$ at a point $p \in M$ in
terms of the behaviour of the asymptotic directions and the
curvature locus at $p$. We relate the affine properties of codimension 2
submanifolds with flat normal bundle with the conformal properties
of hypersurfaces in Euclidean space. We also characterize the semiumbilical,
hypespherical and conformally flat submanifolds of codimension 2 in terms of
their curvature loci.
Publié le : 2010-09-15
Classification:
asymptotic directions,
$\nu$-principal curvature foliation,
umbilicity,
sphericity,
normal curvature,
53A05,
58C25
@article{1282913822,
author = {Nu\~no-Ballesteros
,
J. J. and Romero-Fuster
,
M. C.},
title = {Contact properties of codimension 2 submanifolds with flat normal bundle},
journal = {Rev. Mat. Iberoamericana},
volume = {26},
number = {1},
year = {2010},
pages = { 799-824},
language = {en},
url = {http://dml.mathdoc.fr/item/1282913822}
}
Nuño-Ballesteros
,
J. J.; Romero-Fuster
,
M. C. Contact properties of codimension 2 submanifolds with flat normal bundle. Rev. Mat. Iberoamericana, Tome 26 (2010) no. 1, pp. 799-824. http://gdmltest.u-ga.fr/item/1282913822/