A few affine invariant structures depending only on the second fundamental form relative to arbitrary transversal bundles on submanifolds of the standard affine spaces are introduced. A notion of “local strong convexity” is proposed for arbitrary codimensional submanifolds. In the case of $n$-dimensional submanifolds of $2n$-dimensional real affine spaces, complex structures on the ambient spaces are used as a tool for studying real affine invariants.
Publié le : 2008-05-15
Classification:
Affine invariant,
affine connection,
conformal structure,
ellipse of curvature,
53B25,
53C15
@article{1223057735,
author = {Opozda, Barbara},
title = {Weak geometric structures on submanifolds of affine spaces},
journal = {Tohoku Math. J. (2)},
volume = {60},
number = {1},
year = {2008},
pages = { 383-401},
language = {en},
url = {http://dml.mathdoc.fr/item/1223057735}
}
Opozda, Barbara. Weak geometric structures on submanifolds of affine spaces. Tohoku Math. J. (2), Tome 60 (2008) no. 1, pp. 383-401. http://gdmltest.u-ga.fr/item/1223057735/