8830 



Surfaces defined by Differential Properties 



Theorems. Lie, M. S. Arch. Mth. Ntvd. 3 



(1878) 166-. 

 Theory. Enneper, A. Gott. Nr. (1882) 34-, 



89-. 



. Darboiix, G. C. E. 102 (1886) 151 3-. 

 . Goursat, E. C. B. 105 (1887) 743-. 

 , extension. Lipschitz, R. O. S. [1872-73] 



(x) Crelle J. Mth. 78 (1874) 1-. 

 Transcendental surface. Lichtenfels, 0. von. 



Wien Ak. Sb. 94 (1887) (Ab. 2) 41-. 

 Transformation. Goursat, E. Acta Mth. 11 



(1887-88) 135-, 257-. 

 Transformations. Bianchi, L. Km. B. Ac. 



Line. Ed. 8 (1899) (Sem. 2) 151-. 



8830 Surfaces determined by re- 

 lations of curvature and by 

 other differential properties. 



Condition that lines can be cut orthogonally. 



Cayley, A. [1876] L. Mth. S. P. 8 (1877) 53-. 

 Corresponding surfaces, two classes. Mangeot, 



S. Mathesis 14 (1894) 34-. 

 Determination of all algebraic integral surfaces 



of the differential equation s = inscribed in 



an algebraic developable. Lie, M. S. Arch. 



Mth. Ntvd. 4 (1879) 334-. 

 surfaces admitting continuous system 



of projective transformations. Lie, S. Leip. 



Mth. Ps. B. 47 (1895) 209-. 

 ovaloids by measure of curvature for each 



normal section. Liebmann, H. Gott. Nr. 



(1899) 134-. 

 spiral surfaces by line element. Raffy, L. 



C. E. 112 (1891) 1421-. 

 surface by its 2 fundamental quadratic 



forms. Raffy, L. C. E. 126 (1898) 1852-. 

 one of its two surfaces of centres. 



Hoppe, R. Arch. Mth. Ps. 68 (1882) 256-. 

 surfaces by curvature relations. Lipschitz , 



R. 0. S. Berl. Ak. Sb. (1882) 1077- ; (1883) 



169-, 541-. 



with prescribed expression for line 

 element. Lipschitz, R. Berl. Ak. Sb. (1884) 

 649-. 



system of equal lines of curvature. 



Bricard, R. C. E. 130 (1900) 475-. 

 Developable, surface of centres. Petersson, V. 



Fschr. Mth. (1886) 748-. 



formed by tangent planes along curve on 

 surface. Enneper, A. Gott. Nr. (1869) 207-. 



through 2 given curves, generation. Taylor, 

 H. M. Mess. Mth. 5 (1876) 1-. 



Developables. Rehofovsky, V. Casopis 9 (*1880) 

 31-, 60-, 161-, 223-; Fschr. Mth. (*1880) 

 569-. 



, representation of geodesies on. Puchta, A. 

 Wien Ak. Sb. 97 (1889) (Ab. 2a) 1269-. 



Differential equations of some families of sur- 

 faces. Tanner, H.W. L. [1876-77] Mess. 

 Mth. 6 (1877) 120-. 



geometry, theorem. Padova, E. Mil. I. 

 Lomb. Ed. 23 (1890) 840-. 



Envelope of a surface. Enneper, A. Mth. A. 

 5 (1872) 304- ; Gott. Nr. (1873) 217-. 



8830 



Enveloping surfaces. Garbieri, G. Ven. I. 



At. (*1883-84) 1201-. 

 Fuchsian surfaces. Bianchi, L. Em. B. Ac. 



Line. Ed. 4 (1888) (Sem. 2) 161-. 

 Geodesic representations of surfaces. Liouville, 



R. C. E. 108 (1889) 335-. 

 Geometrical applications of Picard's method of 



successive approximations. Bianchi, L. Em. 



E. Ac. Line. Ed. 3 (1894) (Sem. 1) 143-. 

 Harmonic ruled surfaces. Raffy, L. C. E. 



110 (1890) 223-. 



spirals. Raffy, L. C. E. 112 (1891) 518-. 



surfaces. Raffy, L. Par. S. Mth. Bll. 

 22 (1894) 63-, 84-. 



, class. Raffy, L. C. E. 112 (1891) 



424-. 



surfaces, properties. Raffy, L. Toul. 

 Fac. Se. A. 9 (1895) C, 44 pp. 



Isometric surfaces. Voss, A. Mth. A. 46 



(1895) 97-. 



. Pellet, A. C. E. 124 (1897) 1337-. 



Isometry of lines of curvature. Knoblauch, J. 



Crelle J. Mth. 103 (1888) 40-. 

 Kinematic classification of surfaces according 



to geodesic triangles. Mangoldt, H. von. 



[1882] Freiburg B. 8 (*1882-85) 73-; (x) 



Crelle J. Mth. 94 (1883) 21-. 

 . Weingarten, J. L. G. J. 



Berl. Ak. Sb. (1882) 453-. 

 Liouville's surfaces, characteristic property. 



Stackel, P. Mth. A. 35 (1890) 91-. 

 Locus of centres of curvature. Arndt, F. 



Grunert Arch. 9 (1847) 68-. 

 Orthogonal surfaces. Cayley, A, C. E. 75 



(1872) 177-, 246-, 324-, 381-^1800-. 

 . Vanecek, J. S. Prag Ceske Ak. Fr. 



Jos. Ez. (Tfida 2) 4 (1895) Art. 16, 4 pp. 

 Parallel surfaces. Steiner, J. Berl. B. (1840) 



114-. 



. Roberts, W. C. E. 54 (1862) 797-. 



. Roberts, S. L. Mth. S. P. 4 (1871-73) 



218-. 

 , etc. Combescure, E. Par. EC. Norm. A. 



7 (1878) 409-. 

 , and application to ellipsoid. Tortolini, 



B. Tortolini A. 1 (1850) 5-. 



, theorem, applications. Roberts, W. 

 Ph. Mg. 24 (1862) 39-. 



Partial differential equation, Cayley's, in theory 

 of surfaces. Bianchi, L. Em. E. Ac. Line. 

 Ed. 4 (1888) (Sem. 1) 442-. 



of surfaces of constant curvature. 



Darboux, G. C. E. 97 (1883) 946-. 



equations connected with theory of 

 surfaces. Craig, T. Am. J. Mth. 19 (1897) 

 94-. 



of cylinders. Tanner, H. W. L. 



[1876] Mess. Mth. 6 (1877) 113. 



and representation of surfaces. Dar- 

 boux, G. C. E. 96 (1883) 766-. 



theory of surfaces, relation between. 



Stouff, X. Par. EC. Norm. A. 13 (1896) 9-. 



Euled surface, dependence of characters on 

 characters of guiding curves. Rupp, O. 

 Mth. A. 18 (1881) 366-. 



surfaces. Hachette, J. N. P. Crelle J. 8 

 (1832) 358-. 



642 



