./ Math 151 Lie Geometry Spring 1992 ~ for this course: oA...J Pedoe, Daniel. A course of geometry for colleges and universities [by] D. pedoe. London, Cambridge University Press, 1970. UCSD S & E QA445 .P43 Emphasis on representational geometry and inversive geometry. Easy reading. Near to the approach used in the course. Ch. IV. The representation of circle by points in space of three dimensions. Ch. VI. Mappings of the inversive plane. Ch. VIII. The projective geometry of n dimensions. Ch. IX. The projective generation of conics and quadrics. Relevant articles i ,( 1/ (/' ,{ '" Behnke, Heinrich, 1898- Fundamentals of mathematics / edited by H. Behnke ... [et al.]; translated by S. H. Gould. Cambridge, Mass. : MIT Press, [1974]. UCSD Central QA37.2 .B413 and UCSD S & E QA37.2 .B413 Many interesting articles on various geometries. Easy general reading. Geometries of circled and Lie geometry discussed in: . Ch. 12. Erlanger program and higher geometry. Kunle and Fladt. ~Ch. 13. Group Theory and Geometry. F~enthal and Steiner

Classical references

Blaschke, W.H. Vorlesungen tiber Differentialgeometrie, III Differentialgeometrie der Kreise und Kugeln, Springer Verlag, Berlin, 1929. Very difficult reading. Not available at UCSD.

Coolidge, Julian Lowell, 1873-1954. A treatise on the circle and the sphere. Chelsea Pub. Co., Bronx, N.Y., 1971. UCSD S & E QA484 .C65 1971 Classic 1916 treatise on circles and spheres. Very difficult reading. It is best to translate ideas to modern setting and then provide one's own proofs Lie, Sophus, 1842-1899. Geometrie der Beruhrungstransformationen. Dargestellt von Sophus Lie und Georg Scheffers. Leipzig, B.G. Teubner, 1896. UCSD S & E QA385 .L66

Lie, Sophus, 1842-1899. _ Vorlesungen uber continuierliche Gruppen mit geometrischen und anderen Anwendungen. Bearb. und hrsg. von Georg Scheffers. Leipzig, B.G. Teubner, 1893. UCSD S & E QA385 .L7

Jessop, Charles Minshall, 1861-1939. A treatise on the line complex. New York, Chelsea Pub. Co. [1969]. UCSD S & E QA608 .J58 1903a

Klein, Felix, 1849-1925. Vorlesungen uber hohere Geometrie. 3. Aufl., b~arb. und hrsg. von W. Blaschke. Berlin, J. Springer, 1926. Series title: Die Grundlehren der methematischen wissenschaften in Einzeldarstellungen Bd. 22. UCSD S & E QA601 .K64 1926 -rl>.1",-,~ ,~_., '. - ~ . ----... t.',i--'(~. \ Current references

The Geometric vein : the Coxeter Festschrift / edited by Chandler Davis, Branko Grunbaum, F.A. Sherk with contributions by Patrice Assouad ... [et al.]. New York : Springer-Verlag, c1981. UCSD S & E QA446 .G46 1981 Research articles and expositions. Geometries of circles and Lie geometry closest to the approach used in the course: I. M . Yaglom. On the circular transformations of Mobius, Laguerre, and Lie. pp. 345ff. J. F. Rigby. The geometry of cycles and generalized Laguerre inversion. pp. 355ff. . Related article, more difficult reading: J. B. Wilker. Inversive geometry. pp. 379ff.

Cecil, T. E., Lie Sphere Geometry, Springer Verlag, 1992. ISBN 0-387-97747-3. New release.

Cecil, T. E. and Chern, S.-S., Tautness and Lie Sphere Geometry, Math. Ann., 278 (1987), 381-3.99. Research article.

Cecil, T. E. (Thomas E.), 1945- Tight and taut immersions of manifolds / T.E. Cecil & P.J. Ryan. Boston pitman Advanced Pub. Program, 1985. Series title: Research notes in mathematics; 107. UCSD S & E QA649 .C43 1985

Algebraic projective geometry:

Artin, Emil, 1898-1962. Geometric algebra. New York, Interscience Publishers [1957]. Series title: Interscience tracts in pure and applied mathematics no. 3. UCSD S & E QA685 .A787 Advanced beautiful classic, di;fficult.

Gruenberg, Karl W. . Linear geometry / K. W. Gruenberg, A. J. Weir. 2d ed. New York: Springer-Verlag, 1977. Series title: Graduate texts in mathematics; 49. . UCSD S & E QA564.G721977 Projective geometry using coordinate-free linear algebra. Ch. II. Affine and projective geometry. Ch. III. Isomorhisms. Ch. v. Bilinear forms.

Kaplansky, Irving, 1917- Linear algebra and geometry; a second course. Boston, Allyn and Bacon [1969]. 'UCSD S & E QA251 .K32

Seidenberg, A. (Abraham), 1916- Lectures in projective geometry. Princeton, N.J., Van Nostrand [1962]. Series title: The University series in undergraduate mathematics. UCSD S & E QA471 .S458 Overview of projective geometry with emphasis on 'linear algebra. Especially useful: Chs. V to XIII on analytic projective geometry.

4';( Semple, J. G. and Kneebone, G. T., Algebraic Projective Geometry, Oxford, London, 1952, 1960. ~ classic. Out of print and not at UCSD libraries. Snapper, Ernst, 1913- Metric affine geometry [by] Ernst Snapper [and] Robert J. Troyer. New \.J York,.Academic -Press [1971]. ueSD S & ~ QA477 .S63