[Déformations infinitésimales isospectrales de la grassmannienne des 3-plans dans ]
Ce mémoire a pour cadre la grassmannienne des -plans de , avec , et son espace réduit qui est l’espace symétrique irréductible, quotient de par l’involution envoyant un -plan sur son orthogonal. Un de nos principaux résultats est la construction de déformations infinitésimales isospectrales non triviales sur obtenant ainsi le premier exemple d’espace symétrique irréductible réduit et non infinitésimalement rigide. Nous donnons aussi un critère d’exactitude pour les formes différentielles de degré 1 sur mettant en jeu la nullité d’une transformée de Radon.
We study the real Grassmannian of -planes in , with , and its reduced space. The latter is the irreducible symmetric space , which is the quotient of the space under the action of its isometry which sends a -plane into its orthogonal complement. One of the main results of this monograph asserts that the irreducible symmetric space possesses non-trivial infinitesimal isospectral deformations; it provides us with the first example of an irreducible reduced symmetric space which admits such deformations. We also give a criterion for the exactness of a form of degree one on in terms of a Radon transform.
Keywords: Symmetric space, Grassmannian, Radon transform, infinitesimal isospectral deformation, symmetric form, Guillemin condition
Mot clés : Espace symétrique, grassmannienne, transformée de Radon, déformation isospectrale, forme symétrique, condition de Guillemin
@book{MSMF_2007_2_108__1_0, author = {Gasqui, Jacques and Goldschmidt, Hubert}, title = {Infinitesimal isospectral deformations of the {Grassmannian} of 3-planes in ${\mathbb{R}}^6$}, series = {M\'emoires de la Soci\'et\'e Math\'ematique de France}, publisher = {Soci\'et\'e math\'ematique de France}, number = {108}, year = {2007}, doi = {10.24033/msmf.420}, mrnumber = {2447005}, zbl = {1152.53040}, language = {en}, url = {http://www.numdam.org/item/MSMF_2007_2_108__1_0/} }
TY - BOOK AU - Gasqui, Jacques AU - Goldschmidt, Hubert TI - Infinitesimal isospectral deformations of the Grassmannian of 3-planes in ${\mathbb{R}}^6$ T3 - Mémoires de la Société Mathématique de France PY - 2007 IS - 108 PB - Société mathématique de France UR - http://www.numdam.org/item/MSMF_2007_2_108__1_0/ DO - 10.24033/msmf.420 LA - en ID - MSMF_2007_2_108__1_0 ER -
%0 Book %A Gasqui, Jacques %A Goldschmidt, Hubert %T Infinitesimal isospectral deformations of the Grassmannian of 3-planes in ${\mathbb{R}}^6$ %S Mémoires de la Société Mathématique de France %D 2007 %N 108 %I Société mathématique de France %U http://www.numdam.org/item/MSMF_2007_2_108__1_0/ %R 10.24033/msmf.420 %G en %F MSMF_2007_2_108__1_0
Gasqui, Jacques; Goldschmidt, Hubert. Infinitesimal isospectral deformations of the Grassmannian of 3-planes in ${\mathbb{R}}^6$. Mémoires de la Société Mathématique de France, Série 2, no. 108 (2007), 98 p. doi : 10.24033/msmf.420. http://numdam.org/item/MSMF_2007_2_108__1_0/
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