The main aim of this paper is to compute the index and the nullity of the identity map of $S^n\times S^m$ and $S^n\times T^m$. In order to obtain this we establish a rather general result on the spectrum of the Hodge-Laplacian on $k$-forms on a product manifold, which could prove useful in other contexts.
Publié le : 2000-05-14
Classification:
Harmonic maps,
second variation,
Jacobi fields,
spectrum of the Hodge-Laplacian,
58E20,
53C43,
58J50
@article{1178224608,
author = {Fardoun, Ali and Ratto, Andrea},
title = {On the second variation of the identity map of a product manifold},
journal = {Tohoku Math. J. (2)},
volume = {52},
number = {4},
year = {2000},
pages = { 235-249},
language = {en},
url = {http://dml.mathdoc.fr/item/1178224608}
}
Fardoun, Ali; Ratto, Andrea. On the second variation of the identity map of a product manifold. Tohoku Math. J. (2), Tome 52 (2000) no. 4, pp. 235-249. http://gdmltest.u-ga.fr/item/1178224608/