The fundamental theorem (existence and uniqueness) for submanifolds of real space forms is well-known. We will discuss this theorem for some families of submanifolds in the framework of Grassmann geometries in a unified way. In particular, we show the fundamental theorem for half dimensional totally complex submanifolds of the quaternion projective space $\mathbb{H}P^n$ or the quaternion hyperbolic space $\mathbb{H}H^n$. This result is an affirmative answer to the conjecture by Alekseevsky and Marchiafava.
Publié le : 2007-08-15
Classification:
the fundamental theorem for submanifolds,
totally complex submanifolds,
53B25,
53C26
@article{1277472870,
author = {TSUKADA, Kazumi},
title = {Fundamental theorem for totally complex submanifolds},
journal = {Hokkaido Math. J.},
volume = {36},
number = {4},
year = {2007},
pages = { 641-668},
language = {en},
url = {http://dml.mathdoc.fr/item/1277472870}
}
TSUKADA, Kazumi. Fundamental theorem for totally complex submanifolds. Hokkaido Math. J., Tome 36 (2007) no. 4, pp. 641-668. http://gdmltest.u-ga.fr/item/1277472870/