TY - BOOK UR - http://lib.ugent.be/catalog/ebk01:1000000000788579 ID - ebk01:1000000000788579 ET - Course Book. LA - eng TI - Radon Transforms and the Rigidity of the Grassmannians (AM-156) PY - 2004 SN - 9781400826179 AU - Gasqui, Jacques, author. AU - Goldschmidt, Hubert, author. AB - 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. 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. ER -Download RIS file
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020 | a 9781400826179 | ||
024 | 7 | a 10.1515/9781400826179 2 doi | |
035 | a (DE-B1597)446509 | ||
035 | a (OCoLC)437268713 | ||
040 | a IN-ChSCO b eng c IN-ChSCO e rda | ||
041 | a eng | ||
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100 | 1 | a Gasqui, Jacques, e author. | |
245 | 1 | a Radon Transforms and the Rigidity of the Grassmannians (AM-156) / c Jacques Gasqui, Hubert Goldschmidt. | |
250 | a Course Book. | ||
264 | 1 | a Princeton, N.J. : b Princeton University Press, c [2004] | |
264 | 4 | c Â©2004 | |
300 | a 1 online resource (384 pages) : b illustrations. | ||
336 | a text 2 rdacontent | ||
337 | a computer 2 rdamedia | ||
338 | a online resource 2 rdacarrier | ||
347 | a text file b PDF 2 rda | ||
490 | a Annals of Mathematics Studies, x 0066-2313 ; v 156 | ||
505 | t Frontmatter -- t TABLE OF CONTENTS -- t INTRODUCTION -- t Chapter I. Symmetric Spaces and Einstein Manifolds -- t Chapter II. Radon Transforms on Symmetric Spaces -- t Chapter III. Symmetric Spaces of Rank One -- t Chapter IV. The Real Grassmannians -- t Chapter V. The Complex Quadric -- t Chapter VI. The Rigidity of the Complex Quadric -- t Chapter VII. The Rigidity of the Real Grassmannians -- t Chapter VIII. The Complex Grassmannians -- t Chapter IX. The Rigidity of the Complex Grassmannians -- t Chapter X. Products of Symmetric Spaces -- t References -- t Index. | ||
520 | a 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. 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. | ||
533 | a Electronic reproduction. b Princeton, N.J. : c Princeton University Press, d 2004. n Mode of access: World Wide Web. n System requirements: Web browser. n Access may be restricted to users at subscribing institutions. | ||
538 | a Mode of access: Internet via World Wide Web. | ||
546 | a In English. | ||
588 | a Description based on online resource; title from PDF title page (publisherâ€™s Web site, viewed October 27 2015) | ||
650 | a MATHEMATICS v Functional Analysis. | ||
650 | a MATHEMATICS v Geometry v Differential. | ||
650 | a Radon transforms. | ||
650 | a Rigidity (Geometry) | ||
650 | 4 | a Geometry and Topology. | |
650 | 4 | a Grassmann manifolds. | |
650 | 4 | a Mathematics. | |
650 | 4 | a Mathematik. | |
650 | 4 | a Radon transforms. | |
650 | 4 | a Rigidity (Geometry) | |
700 | 1 | a Goldschmidt, Hubert, e author. | |
773 | 8 | i Title is part of eBook package: d De Gruyter t Princeton Annals of Mathematics Backlist eBook Package z 978-3-11-049491-4 | |
773 | 8 | i Title is part of eBook package: d De Gruyter t Princeton eBook Package Backlist 2000-2013 z 978-3-11-044250-2 | |
773 | 8 | i Title is part of eBook package: d De Gruyter t Princeton eBook Package Backlist 2000-2014 z 978-3-11-045953-1 | |
773 | 8 | i Title is part of eBook package: d De Gruyter t Princeton Univ. Press eBook Package 2000-2013 z 978-3-11-041343-4 | |
830 | a Annals of Mathematics Studies ; v 156. | ||
856 | 4 | u https://doi.org/10.1515/9781400826179 | |
856 | 4 | 2 | 3 Cover u https://www.degruyter.com/doc/cover/9781400826179.jpg |
912 | a 978-3-11-041343-4 Princeton Univ. Press eBook Package 2000-2013 | ||
912 | a 978-3-11-044250-2 Princeton eBook Package Backlist 2000-2013 | ||
912 | a 978-3-11-045953-1 Princeton eBook Package Backlist 2000-2014 | ||
912 | a 978-3-11-049491-4 Princeton Annals of Mathematics Backlist eBook Package | ||
912 | a GBV-deGruyter-alles | ||
912 | a GBV-deGruyter-PDA12STME | ||
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