He was active in representation theory, general concepts of quantization and coherent states, supersymmetry and supermanifolds, among other fields. Skip to main content Skip to table of contents. Advertisement Hide.
Conference proceedings. Papers Table of contents 39 papers About About these proceedings Table of contents Search within book. Front Matter Pages i-xix. Front Matter Pages Felix Alexandrovich Berezin and His Work. Pages Exhausting Formal Quantization Procedures. On One Result of F. They should know how to proceed…. Sauvegarder l'image.
Date: pages: ISBN: Its primary focus is the spectral rigidity problem: Can the metric of a giv. Similar books. Public Folders 0. Private Folders 0. Courses 0. Comments 0.
Radon Transforms and the Rigidity of the Grassmannians (AM-156)
This book provides the first unified examination of the relationship between Radon transforms on symmetric spaces of compact type and the infinitesimal versions of two fundamental rigidity problems in Riemannian geometry. Its primary focus is the spectral rigidity problem: Can the metric of a given Riemannian symmetric space of compact type be characterized by means of the spectrum of its Laplacian? It also addresses a question rooted in the Blaschke problem: Is a Riemannian metric on a projective space whose geodesics are all closed and of the same length isometric to the canonical metric?
The authors comprehensively treat the results concerning Radon transforms and the infinitesimal versions of these two problems. Their main result implies that most Grassmannians are spectrally rigid to the first order.
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The authors exploit the theory of overdetermined partial differential equations and harmonic analysis on symmetric spaces to provide criteria for infinitesimal rigidity that apply to a large class of spaces. A substantial amount of basic material about Riemannian geometry, symmetric spaces, and Radon transforms is included in a clear and elegant presentation that will be useful to researchers and advanced students in differential geometry.
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Symmetric spaces and Einstein manifolds 1. Riemannian manifolds 1 2. Einstein manifolds 15 3. Symmetric spaces 19 4. Radon transforms on symmetric spaces 1. Outline 32 2.
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Homogeneous vector bundles and harmonic analysis 32 3. The Guillemin and zero-energy conditions 36 4. Radon transforms 41 5. Radon transforms and harmonic analysis 50 6. Lie algebras 58 7. Irreducible symmetric spaces 59 8.
Symmetric spaces of rank one 1. Flat tori 75 2. The projective spaces 83 3. The real projective space 89 4. The complex projective space 94 5.
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The rigidity of the complex projective space 6. The real Grassmannians 1. The real Grassmannians 2. The Complex Quadradic 1.
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Outline 2. The complex quadric viewed as a symmetric space 3. The complex quadric viewed as a complex hypersurface 4. The complex quadric and the real Grassmannians 6. Totally geodesic surfaces and the infinitesimal orbit of the curvature 7. Multiplicities 8. Vanishing results for symmetric forms 9. The rigidity of the complex quadric 1. Total geodesic at tori of the complex quadric 3.
Symmetric forms on the complex quadric 4. Computing integrals of symmetric forms 5. Computing integrals of odd symmetric forms 6. Bounds for the dimensions of spaces of symmetric forms 7. The complex quadric of dimension three 8. The rigidity of the complex quadric 9.
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Other proofs of the infinitesimal rigidity of the quadric The complex quadric of dimension four The rigidity of the real Grassmannians 1. The rigidity of the real Grassmannians 2. The complex Grassmannians 1.
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