**Memoires de la Societe Mathematique de France**

Volume: 108;
2007;
92 pp;
Softcover

MSC: Primary 44; 53; 58;
**Print ISBN: 978-2-85629-232-7
Product Code: SMFMEM/108**

List Price: $38.00

Individual Member Price: $34.20

# Infinitesimal Isospectral Deformations of the Grassmannian of 3-Planes in $\mathbb{R}^{6}$

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*Jacques Gasqui; Hubert Goldschmidt*

A publication of the Société Mathématique de France

The authors study the real Grassmannian \(G^\mathbb{R}_{n,n}\) of \(n\)-planes in \(\mathbb{R}^{2n}\), with \(n\ge 3\), and its reduced space. The latter is the irreducible symmetric space \(\bar G^\mathbb{R}_{n,n}\), which is the quotient of the space \(G^\mathbb{R}_{n,n}\) under the action of its isometry which sends a \(n\)-plane} into its orthogonal complement. One of the main results of this monograph asserts that the irreducible symmetric space \(\bar G^\mathbb{R}_{3,3}\) possesses non-trivial infinitesimal isospectral deformations; it provides the first example of an irreducible reduced symmetric space which admits such deformations. The authors also give a criterion for the exactness of a form of degree one on \(\bar G^\mathbb{R}_{n,n}\) in terms of a Radon transform.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

#### Table of Contents

# Table of Contents

## Infinitesimal Isospectral Deformations of the Grassmannian of 3-Planes in $\mathbb{R}^{6}$

#### Readership

Graduate students and research mathematicians interested in analysis.