Algebra und Geometrie 2. Moduln und Algebren by von Oniscik A.L., Sulanke R. PDF

By von Oniscik A.L., Sulanke R.

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14(1935), pp. 237-243. 2. P. BTJZANO, Invariante proiettivo di una particolare coppia di elementi di superficie, BoUettino della Unione Matematica Italiana, vol. 14(1935), pp. 93-98. 3. C. C. HSIUNG, Projective differential geometry of a pair of plane curves, this Journal, vol. 10 (1943), pp. 539-546. NATIONAL UNIVERSITY OF C H E K I A N G , M E I T A N , K W E I C H O W , C H I N A . PROJECTIVE INVARIANTS OF INTERSECTION OF CERTAIN PAIRS OF SURFACES CHUAN-CHIH HSIUNG 1. Introduction. In a recent paper [2] 1 the author has shown the existence, together with metric and projective characterizations, 2 of a unique projective invariant determined by the neighborhood of the second order of two surfaces Si, S2 at an ordinary point 0 in ordinary space when the tangent planes n, r 2 of the surfaces Si, 5 2 at the point 0 are distinct and the line / of intersection of the two tangent planes T\, T 2 does not coincide with any one of the asymptotic tangents of the surfaces Si, St at the point 0.

Case III. expansions: Ii y£ 0, J 2 = 0. )* + « € ) ' + "• • _ / \ 2 / \ 5 * / \ 6 PLANE CURVES 545 in which the three coefficients al , a*, a* can be expressed also in terms of the invariant 7i and two cross ratios similar to (36), (37). Case TV. It = 0, 72 = 0. Combination of the expansions of the curve C in Case II and the curve C* in Case III yields the required canonical power series expansions for this case. )*+£ © ' + ••• • in which the four coefficients at , a4 , a*, a* can be expressed in terms of the two cross ratios (36), (37) and two analogous ones as in the two preceding cases.

P. Buzano, Invariante proiettivo di una particolare coppia di elementi di superficie, Bollettino della Unione Matematica Italiana vol. 14 (1935) pp. 93-98. 3. C. C. Hsiung, Projective invariants of a pair of surfaces, t o appear in Amer. J. Math. 4. M. Mascalchi, Un nuovo invariante proiettivo di contatto di 'due superficie, Bollettino della Unione Matematica Italiana vol. 13 (1934) pp. 45-49. 5. R. Mehmke, Einige Satze iiber die raumliche Collineation und Affinitat, welche sich auf die Kriimmung von Kurven und FtSchen beziehen, Schlomilchs Zeitschrift fur Mathematik und Physik vol.