{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T16:36:40Z","timestamp":1649176600348},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"3-4","license":[{"start":{"date-parts":[[1995,6,1]],"date-time":"1995-06-01T00:00:00Z","timestamp":801964800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[1995,6]]},"DOI":"10.1007\/bf02574059","type":"journal-article","created":{"date-parts":[[2007,3,22]],"date-time":"2007-03-22T12:15:26Z","timestamp":1174565726000},"page":"517-527","source":"Crossref","is-referenced-by-count":3,"title":["A helmholtz-lie type characterization of ellipsoids, I"],"prefix":"10.1007","volume":"13","author":[{"given":"P. M.","family":"Gruber","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[1995,6,1]]},"reference":[{"key":"BF02574059_CR1","first-page":"3","volume":"6","author":"A. D. Alexandrov","year":"1939","unstructured":"Alexandrov, A. D.: Almost everywhere existence of the second differential of a convex function and some properties of convex surfaces connected with it,Uchen. Zap Leningrad. Gos. Univ. Math. Ser. 6 (1939), 3\u201335.","journal-title":"Uchen. Zap Leningrad. Gos. Univ. Math. Ser."},{"key":"BF02574059_CR2","doi-asserted-by":"crossref","first-page":"17","DOI":"10.4064\/sm-9-1-17-22","volume":"9","author":"H. Auerbach","year":"1940","unstructured":"Auerbach, H.: Sur une propri\u00e9t\u00e9 caracteristique de l'ellipsoide,Studia Math. 9 (1940), 17\u201322.","journal-title":"Studia Math."},{"key":"BF02574059_CR3","unstructured":"Berger, M.: Seules les quadriques admettent des caustiques,Bull. Soc. Math. France, to appear."},{"key":"BF02574059_CR4","first-page":"18","volume":"70","author":"W. Blaschke","year":"1918","unstructured":"Blaschke, W.: \u00dcber affine Geometrie XII: Von den Eifl\u00e4chen,Ber. Ges. Wiss. Leipzig 70 (1918), 18\u201337;Gesammelte Werke, vol. 4, Thales-Verlag, Essen, 1985, pp. 157\u2013176.","journal-title":"Ber. Ges. Wiss. Leipzig"},{"key":"BF02574059_CR5","unstructured":"Brunn, H.:\u00dcber Kurven ohne Wendepunkte, Habilitationsschrift, M\u00fcnchen, 1889."},{"key":"BF02574059_CR6","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1007\/BF02568163","volume":"51","author":"G. R. Burton","year":"1976","unstructured":"Burton, G. R.: On the sum of a zonotope and an ellipsoid,Comment. Math. Helv. 51 (1976), 369\u2013387.","journal-title":"Comment. Math. Helv."},{"key":"BF02574059_CR7","doi-asserted-by":"crossref","first-page":"303","DOI":"10.2140\/pjm.1979.81.303","volume":"81","author":"G. R. Burton","year":"1979","unstructured":"Burton, G. R.: Congruent sections of a convex body,Pacific J. Math. 81 (1979), 303\u2013316.","journal-title":"Pacific J. Math."},{"key":"BF02574059_CR8","first-page":"52","volume":"53","author":"H. Busemann","year":"1967","unstructured":"Busemann, H.: Timelike spaces,Dissertationes Math. (Rozprawy Mat.) 53 (1967), 52.","journal-title":"Dissertationes Math. (Rozprawy Mat.)"},{"key":"BF02574059_CR9","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1007\/BF01899996","volume":"8","author":"L. Danzer","year":"1957","unstructured":"Danzer, L., Laugwitz, D., Lenz, H.: \u00dcber das L\u00f6wnersche Ellipsoid und sein Analogon unter den einem Eik\u00f6rper einbeschriebenen Ellipsoiden,Arch. Math. 8 (1957), 214\u2013219.","journal-title":"Arch. Math."},{"key":"BF02574059_CR10","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1007\/BF01187949","volume":"63","author":"H. Freudenthal","year":"1956","unstructured":"Freudenthal, H.: Neuere Fassung des Riemann-Helmholtz-Lieschen Raumproblems,Math. Z. 63 (1956), 374\u2013405.","journal-title":"Math. Z."},{"key":"BF02574059_CR11","volume-title":"Matrix Computations","author":"G. H. Golub","year":"1989","unstructured":"Golub, G. H., Van Loan, Ch. F.:Matrix Computations, Johns Hopkins University Press, Baltimore, MD, 1989."},{"key":"BF02574059_CR12","first-page":"61","volume":"265","author":"P. M. Gruber","year":"1974","unstructured":"Gruber, P. M.: \u00dcber kennzeichnende Eigenschaften von euklidischen R\u00e4umen und Ellipsoiden, I,J. Reine Angew. Math. 265 (1974), 61\u201383.","journal-title":"J. Reine Angew. Math."},{"key":"BF02574059_CR13","first-page":"9","volume-title":"Jahrb. \u00dcberblicke Math. 1976","author":"P. M. Gruber","year":"1976","unstructured":"Gruber, P. M., H\u00f6binger, J.: Kennzeichnungen von Ellipsoiden mit Anwendungen, in:Jahrb. \u00dcberblicke Math. 1976, Bibliographisches Institut, Mannheim, 1976, pp. 9\u201329."},{"key":"BF02574059_CR14","unstructured":"Helmholtz, H. von: \u00dcber die Thatsachen, die der Geometrie zum Grunde liegen,Nachr. Ges. Wiss. G\u00f6ttingen 1868, 193\u2013221;Wissenschaftliche Abhandlungen, vol. 2, J. A. Barth, Leipzig, 1883, pp. 618\u2013639."},{"key":"BF02574059_CR15","volume-title":"Differentialgeometrie in Vektorr\u00e4umen","author":"D. Laugwitz","year":"1965","unstructured":"Laugwitz, D.:Differentialgeometrie in Vektorr\u00e4umen, Vieweg, Braunschweig, 1965."},{"key":"BF02574059_CR16","first-page":"284","volume":"42","author":"S. Lie","year":"1890","unstructured":"Lie, S.: \u00dcber die Grundlagen der Geometrie,Ber. Ges. Wiss. Lepizig 42 (1890), 284\u2013321, 355\u2013418;Gesammelte Abhandlungen, vol. 2, Teubner, Leipzig, Aschehoug, Oslo, 1937, pp. 380\u2013468.","journal-title":"Ber. Ges. Wiss. Lepizig"},{"key":"BF02574059_CR17","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/BF01299036","volume":"74","author":"P. Mani","year":"1970","unstructured":"Mani, P.: Fields of planar bodies tangent to spheres,Monatsh. Math. 74 (1970), 145\u2013149.","journal-title":"Monatsh. Math."},{"key":"BF02574059_CR18","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1007\/978-3-0348-5858-8_11","volume-title":"Convexity and Its Applications","author":"C. Petty","year":"1983","unstructured":"Petty, C.: Ellipsoids, in:Convexity and Its Applications, Birkh\u00e4user, Basel, 1983, pp. 264\u2013276."},{"key":"BF02574059_CR19","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1007\/978-3-0348-5765-9_1","volume-title":"Contributions to Geometry","author":"R. Schneider","year":"1979","unstructured":"Schneider, R.: Boundary structure and curvature of convex bodies, in:Contributions to Geometry, Birkh\u00e4user, Basel, 1979, pp. 13\u201359."},{"key":"BF02574059_CR20","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511526282","volume-title":"Convex Bodies: The Brunn-Minkowski Theory","author":"R. Schneider","year":"1993","unstructured":"Schneider, R.:Convex Bodies: The Brunn-Minkowski Theory, Cambridge University Press, Cambridge, 1993."},{"key":"BF02574059_CR21","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1137\/1015095","volume":"15","author":"G. W. Stewart","year":"1973","unstructured":"Stewart, G. W.: Error and perturbation bounds for subspaces associated with certain eigenvalue problems.SIAM Rev. 15 (1973), 727\u2013764.","journal-title":"SIAM Rev."},{"key":"BF02574059_CR22","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/BF02568121","volume":"20","author":"W. S\u00fcss","year":"1947","unstructured":"S\u00fcss, W.: Kennzeichnende Eigenschaften der Kugel als Folgerungen eines Brouwerschen Fixpunktsatzes,Comment. Math. Helv. 20 (1947), 61\u201364.","journal-title":"Comment. Math. Helv."}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02574059.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02574059\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02574059","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,18]],"date-time":"2019-05-18T16:19:18Z","timestamp":1558196358000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02574059"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,6]]},"references-count":22,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[1995,6]]}},"alternative-id":["BF02574059"],"URL":"https:\/\/doi.org\/10.1007\/bf02574059","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,6]]}}}