LEADER 07482nam 2201885 a 450 001 9910778216403321 005 20200520144314.0 010 $a1-282-15898-8 010 $a9786612158988 010 $a1-4008-2617-9 024 7 $a10.1515/9781400826179 035 $a(CKB)1000000000788579 035 $a(EBL)457718 035 $a(OCoLC)437268713 035 $a(SSID)ssj0000232337 035 $a(PQKBManifestationID)11173535 035 $a(PQKBTitleCode)TC0000232337 035 $a(PQKBWorkID)10214021 035 $a(PQKB)10369477 035 $a(DE-B1597)446509 035 $a(OCoLC)979629195 035 $a(DE-B1597)9781400826179 035 $a(Au-PeEL)EBL457718 035 $a(CaPaEBR)ebr10312481 035 $a(CaONFJC)MIL215898 035 $a(MiAaPQ)EBC457718 035 $a(PPN)199244715 035 $a(EXLCZ)991000000000788579 100 $a20031027d2004 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aRadon transforms and the rigidity of the Grassmannians$b[electronic resource] /$fJacques Gasqui and Hubert Goldschmidt 205 $aCourse Book 210 $aPrinceton, N.J. $cPrinceton University Press$d2004 215 $a1 online resource (385 p.) 225 1 $aAnnals of mathematics studies ;$vno. 156 300 $aDescription based upon print version of record. 311 $a0-691-11898-1 311 $a0-691-11899-X 320 $aIncludes bibliographical references (p. [357]-361) and index. 327 $t Frontmatter -- $tTABLE OF CONTENTS -- $tINTRODUCTION -- $tChapter I. Symmetric Spaces and Einstein Manifolds -- $tChapter II. Radon Transforms on Symmetric Spaces -- $tChapter III. Symmetric Spaces of Rank One -- $tChapter IV. The Real Grassmannians -- $tChapter V. The Complex Quadric -- $tChapter VI. The Rigidity of the Complex Quadric -- $tChapter VII. The Rigidity of the Real Grassmannians -- $tChapter VIII. The Complex Grassmannians -- $tChapter IX. The Rigidity of the Complex Grassmannians -- $tChapter X. Products of Symmetric Spaces -- $tReferences -- $tIndex 330 $aThis book provides the first unified examination of the relationship between Radon transforms on symmetric spaces of compact type and the infinitesimal versions of two fundamental rigidity problems in Riemannian geometry. Its primary focus is the spectral rigidity problem: Can the metric of a given Riemannian symmetric space of compact type be characterized by means of the spectrum of its Laplacian? It also addresses a question rooted in the Blaschke problem: Is a Riemannian metric on a projective space whose geodesics are all closed and of the same length isometric to the canonical metric? The authors comprehensively treat the results concerning Radon transforms and the infinitesimal versions of these two problems. Their main result implies that most Grassmannians are spectrally rigid to the first order. This is particularly important, for there are still few isospectrality results for positively curved spaces and these are the first such results for symmetric spaces of compact type of rank ?1. The authors exploit the theory of overdetermined partial differential equations and harmonic analysis on symmetric spaces to provide criteria for infinitesimal rigidity that apply to a large class of spaces. A substantial amount of basic material about Riemannian geometry, symmetric spaces, and Radon transforms is included in a clear and elegant presentation that will be useful to researchers and advanced students in differential geometry. 410 0$aAnnals of mathematics studies ;$vno. 156. 606 $aRadon transforms 606 $aGrassmann manifolds 610 $aAdjoint. 610 $aAutomorphism. 610 $aCartan decomposition. 610 $aCartan subalgebra. 610 $aCasimir element. 610 $aClosed geodesic. 610 $aCohomology. 610 $aCommutative property. 610 $aComplex manifold. 610 $aComplex number. 610 $aComplex projective plane. 610 $aComplex projective space. 610 $aComplex vector bundle. 610 $aComplexification. 610 $aComputation. 610 $aConstant curvature. 610 $aCoset. 610 $aCovering space. 610 $aCurvature. 610 $aDeterminant. 610 $aDiagram (category theory). 610 $aDiffeomorphism. 610 $aDifferential form. 610 $aDifferential geometry. 610 $aDifferential operator. 610 $aDimension (vector space). 610 $aDot product. 610 $aEigenvalues and eigenvectors. 610 $aEinstein manifold. 610 $aElliptic operator. 610 $aEndomorphism. 610 $aEquivalence class. 610 $aEven and odd functions. 610 $aExactness. 610 $aExistential quantification. 610 $aG-module. 610 $aGeometry. 610 $aGrassmannian. 610 $aHarmonic analysis. 610 $aHermitian symmetric space. 610 $aHodge dual. 610 $aHomogeneous space. 610 $aIdentity element. 610 $aImplicit function. 610 $aInjective function. 610 $aInteger. 610 $aIntegral. 610 $aIsometry. 610 $aKilling form. 610 $aKilling vector field. 610 $aLemma (mathematics). 610 $aLie algebra. 610 $aLie derivative. 610 $aLine bundle. 610 $aMathematical induction. 610 $aMorphism. 610 $aOpen set. 610 $aOrthogonal complement. 610 $aOrthonormal basis. 610 $aOrthonormality. 610 $aParity (mathematics). 610 $aPartial differential equation. 610 $aProjection (linear algebra). 610 $aProjective space. 610 $aQuadric. 610 $aQuaternionic projective space. 610 $aQuotient space (topology). 610 $aRadon transform. 610 $aReal number. 610 $aReal projective plane. 610 $aReal projective space. 610 $aReal structure. 610 $aRemainder. 610 $aRestriction (mathematics). 610 $aRiemann curvature tensor. 610 $aRiemann sphere. 610 $aRiemannian manifold. 610 $aRigidity (mathematics). 610 $aScalar curvature. 610 $aSecond fundamental form. 610 $aSimple Lie group. 610 $aStandard basis. 610 $aStokes' theorem. 610 $aSubgroup. 610 $aSubmanifold. 610 $aSymmetric space. 610 $aTangent bundle. 610 $aTangent space. 610 $aTangent vector. 610 $aTensor. 610 $aTheorem. 610 $aTopological group. 610 $aTorus. 610 $aUnit vector. 610 $aUnitary group. 610 $aVector bundle. 610 $aVector field. 610 $aVector space. 610 $aX-ray transform. 610 $aZero of a function. 615 0$aRadon transforms. 615 0$aGrassmann manifolds. 676 $a515/.723 700 $aGasqui$b Jacques$056874 701 $aGoldschmidt$b Hubert$f1942-$056875 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910778216403321 996 $aRadon transforms and the rigidity of the grassmannians$9670617 997 $aUNINA