A lower bound for the class number of $P^n(\pmb{C})$ and $P^n(\pmb{H})$
AGAOKA, Yoshio ; KANEDA, Eiji
Hokkaido Math. J., Tome 35 (2006) no. 1, p. 753-766 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
We obtain new lower bounds on the codimension of local isometric imbeddings of complex and quaternion projective spaces. We show that any open set of the complex projective space $P^n(\pmb{C})$ (resp. quaternion projective space $P^n(\pmb{H})$) cannot be locally isometrically imbedded into the euclidean space of dimension $4n-3$ (resp. $8n-4$). These estimates improve the previously known results obtained in [2] and [7].
Publié le : 2006-11-15
Classification:  curvature invariant,  isometric imbedding,  complex projective space,  quaternion projective space,  root space decomposition,  53C35,  53B25,  17B20 
@article{1285766428,
     author = {AGAOKA, Yoshio and KANEDA, Eiji},
     title = {A lower bound for the class number of $P^n(\pmb{C})$ and $P^n(\pmb{H})$},
     journal = {Hokkaido Math. J.},
     volume = {35},
     number = {1},
     year = {2006},
     pages = { 753-766},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1285766428}
}

AGAOKA, Yoshio; KANEDA, Eiji. A lower bound for the class number of $P^n(\pmb{C})$ and $P^n(\pmb{H})$. Hokkaido Math. J., Tome 35 (2006) no. 1, pp.  753-766. http://gdmltest.u-ga.fr/item/1285766428/