Pseudo-minkowski differential geometry
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Summary
Minkowski geometry is studied by the method of moving frames.
Keywords
Differential Geometry Minkowski Geometry
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Bibliography
- [1]W. Blaschke,Kreis und Kugel, Chelsea, New York, 1949.Google Scholar
- [2]-- --Integralgeometric I, II, Reprint Chelsea, New York, 1949.Google Scholar
- [3]T. Bonnesen undW. Fenchel,Theorie der Konvexen Körper, « Erg. Math. », 3 (1), Springer, Berlin, 1934, reprint New York 1948.MATHGoogle Scholar
- [4]R. C. Bose,A Note on the convex oval, « Bull. Calcutta Math. Soc. »,27, 1935, 54–60,Google Scholar
- [5]H. Busemann,The Foundations of Minkowski geometry « Comment Math. Helv. »,24, 1950, 156–871.MATHMathSciNetGoogle Scholar
- [6]—— ——,Isoperimetric problems in the Minkowski plane, « Amer. J. Math. »,69, 1947, 836–871.MathSciNetGoogle Scholar
- [7]-- --,Angular measure and integral curvature, Canad. J. Math. 1 », 1949, 279–296.Google Scholar
- [8]—— ——,On geodesic curvature in two-dimensional Finsler spaces, « Annali di Mat. », (4) 31, 1950, 281–296.MATHMathSciNetGoogle Scholar
- [8a]—— ——,Areas in affine space. Rend. Circ. Mat. Palermo (2) 9, 1960, 226–242.MATHMathSciNetCrossRefGoogle Scholar
- [9]E. Cartan,Sur la possibilité de plonger un espace riemannien donné dans un espace Euclidien, « Oeuvres complètes ». III/2, 1091–1098.Google Scholar
- [10]—— ——,Les espaces de Finsler, Hermann, Paris, 1934.MATHGoogle Scholar
- [11]C. B. S. Cavallin, Probs. 6571, 6598,Mathematical Question from the « Educational times », Sol.,36, 1881, 40 42.Google Scholar
- [12]G. D. Chakerian andS. K. Stein,The centroid of a homogeneous wire, Announcement 63T-372, Notices A M.S.10, 1963, 587–588.Google Scholar
- [13]M. W. Crofton,On the theory of local probability, applied to straight lines drawn at random in a plane; the methods used being also extended to the proof of certain new theoremq in the integral calculus, « Phil. Trans. Roy. Soc. London »,158, 1868, 188–199,Google Scholar
- [14]H, Guggenheimer,Differential Geometry, McGraw-Hill, New York, 1963.MATHGoogle Scholar
- [15]H. Hadwiger,Vorlesungen über Inhalt, Oberfläche und Isoperimetrie. Springer, Berlin. 1957.MATHGoogle Scholar
- [16]T. Hayashi,Some geometrical applications of Fourier series, « Rend. Circ. Math. Palermo »,50, 1926, 96–102.MATHCrossRefGoogle Scholar
- [17]A. Hurwitz, Uber die Fourierschen Konstanten intergrierbarer Funktionen, « Math. Ann. »,57, 1903, 425–446.CrossRefMATHMathSciNetGoogle Scholar
- [18]H. Lebesgue, Exposition d'un mémoire de M. W. Crofton, « Nouvelles Annales de Math » (4)12, 1912, 481–502.MATHGoogle Scholar
- [19]G. Masotti Biggiogero, Nuove formule di geometria integrale relative agli ovali, « Ann. di Mat. » (4)58, 1962, 85–108.MATHMathSciNetGoogle Scholar
- [20]—— —— Sulla geometria integrale: generalizzazione di formule di Crofton, Lebesgue e Santalò, « Rev. Uniòn Mat. Argentina y Asoc. Fis. Argent. », vol. XVII de Homenaje a Beppo Levi, 1955, 125–134.MathSciNetGoogle Scholar
- [21]—— ——, Su alcune formule di Geometria integrale, « Rend. Mat. Appl. » (5)14, 1955, 280–288.MATHMathSciNetGoogle Scholar
- [22]—— ——, Nuove formule di geometria integrale relative agli ovaloidi, « Rend. Ist. Lombardo, Acc. Sci. Lett., Cl. di Sci. (A) » 96, 1962, 666–685.MATHMathSciNetGoogle Scholar
- [23]E. Meissner, Uber Punktmengen konstanter Breite, « Vierteljahrsschrift Natf. Ges. Zürich56 », 1911, 42–50.MATHGoogle Scholar
- [24]—— ——, Uber die Anwendung von Fourier-Reihen auf einige Aufgaben der Geomeirie und Kinematik, « Vierteljahrsschr. Naft. Ges. Zürich54 », 1909, 309–329.Google Scholar
- [25]C. M. Petty,On the geometry of the Minkowski plane, « Riv. Mat. Univ. Parma6 », 1955, 269–292.MATHMathSciNetGoogle Scholar
- [26]C. M. Petty andJ. M. Barry,Geometrical approach to the second order linear differential equation, « Canad. J. Math.14 », 1962, 349–358.MathSciNetMATHGoogle Scholar
- [27]J. Radon, Uber eine besondere Art ebener konvexer Kurven, Leipz Ber.68, 1916, 123–128.MATHGoogle Scholar
- [28]H. Rund,The differential geometry of Finsler spaces, Springer, Berlin, 1959.MATHGoogle Scholar
- [29]L. A. Santalò, Quelques formules integrales dans la plan et dans l'espace. « Abh. Math. Sem. Hamburg13 », 1940, 344–356.MATHGoogle Scholar
- [30]L. A. Santalò, Un invariante afín para los cuerpos convexos del espacio de n dimensiones, « Port. Math8 », 1949, 155–161.MATHGoogle Scholar
- [31]M. Sayrafiezadhe,Master's thesis University of Minnesota.Google Scholar
- [32]J. Steiner, Von dem Krümmungs-Schwerpuncte ebener Kurven, « J. reine angew. Math. (Crelle) »,21, 1840, 33–63.MATHGoogle Scholar
- [33]W. Süss, Zur relativen Differentialgeometrie, I, « Japan J. Math. 4 », 1927, 57–76.MATHGoogle Scholar
- [34]—— ——, Zur relativen Differentialgeometrie, IV, « Tohoku Math. J. 29 », 1928, 359–362.MATHGoogle Scholar
- [35]—— ——, Affine nnd Minkowskische Geometrie eines ebenen Variationsproblems, « Arch. Math.5 », 1954, 441–446.CrossRefMATHMathSciNetGoogle Scholar
- [36]J. J. Sylvester,On a funicular solution to Buffon's « problem of the needle » in its most general form, « Collected Math. Papers », vol.4, 663–679.Google Scholar
- [37]W. Vogt, Uber monotongekrümmte Kurven, « J. reinr angew. Math. (Crelle)144 », 1914, 239–248.MATHGoogle Scholar
- [38]E. M. Zaustinsky,Spaces with non-symmetric distances, « Memoires A.M.S. no.34 », 1959.Google Scholar
- [39]K. Zindler, Uber konvexe Gebilde I, II, « Mh. Math. Phys. 30 », 1920, 87–102; 31, 1921, 25–27.MATHMathSciNetGoogle Scholar
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© Nicola Zanichelli Editore 1965