Laguerre geometry of surfaces with plane lines of curvature

Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg

Volumn 69, Issue , 1999, Pages 123-138

  Musso, Emilio ^a   Nicolodi, Lorenzo ^b  

^a UNIVERSITY OF L'AQUILA   (Italy)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

L isothermic surfaces; L minimal surfaces; Laguerre geometry; Plane curvature lines

Indexed keywords

EID: 0002369538     PISSN: 00255858     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02940867     Document Type: Article

References (20)

1. P. ADAM, Sur les surfaces isothermiques a lignes de courbure planes dans un systéme ou dans les deux systémes. Ann. scient. Éc. Norm. Sup. 10 (1893), 319-358.
2. L. BIANCHI, Lezioni di geometria differenziale. Vol. I, Zanichelli, 1927.
3. W. BLASCHKE, Vorlesungen über Differentialgeometrie und geometrische Grundlagen von Einsteins Relativitätstheorie. Springer, 1929.
4. _, Über die Geometrie von Laguerre, I, II, III. Abh. Math. Sem. Univ. Hamburg 3 (1924), 176-194, 195-212, 4 (1925), 1-12.
5. _, Über die Geometrie von Laguerre, I, II, III. Abh. Math. Sem. Univ. Hamburg 3 (1924), 176-194, 195-212, 4 (1925), 1-12.
6. R. L. BRYANT, S. S. CHERN and P. A. GRIFFITHS, Exterior differential systems. Proceedings of 1980 Beijing DD-Symposium 1, 219-338, Gordon and Breach 1982.
7. F. BURSTALL, U. HERTRICH-JEROMIN, F. PEDIT, and U. PINKALL, Curved flats and isothermic surfaces. Math. Z. 225 (1997), 199-209.
8. P. CALAPSO, Sulle superficie a linee di curvatura isoterme. Rend. Circ. Mat. Palermo 17 (1903), 273-286.
9. T. E. CECIL, Lie sphere geometry with applications to submanifolds. Springer, 1992.
10. 3 as soliton surfaces. Physics Letters A 205 (1995), 37-43.
11. G. DARBOUX, Leçons sur la théorie générale des surfaces. Chelsea, 1972.
12. L. P. EISENHART, A treatise on the differential geometry of curves and surfaces. Dover Publications, 1960.
13. P. A. GRIFFITHS, On Cartan's method of Lie groups and moving frames as applied to uniqueness and existence questions in differential geometry. Duke Math. J. 41 (1974), 775-814.
14. G. R. JENSEN, Deformation of submanifolds in homogeneous spaces. J. Differential Geom. 16 (1981), 213-246.
15. P. MERCATANTI, Sulle superficie di Bonnet. Giornale di Matematiche 42 (1904), 125-148.
16. E. MUSSO and L. NICOLODI, L-minimal canal surfaces. Rend. Matematica 15 (1995), 421-445. ggg
17. _, A variational problem for surfaces in Laguerre geometry. Trans. Amer Math. Soc. 348 (1996), 4321-1337.
18. _, Isothermal surfaces in Laguerre geometry. Boll. Un. Mat. Ital., (7) II-B, Suppl. fasc. 2 (1997), 125-144.
19. _, On the equation defining isothermic surfaces in Laguerre geometry. New Develpments in Differential Geometry, Budapest 1996, Kluver Academic Publishers, 285-294.
20. K. TENENBLAT, Transformations of manifolds and applications to differential equations. International Conference on Differential Geometry, IMPA, Rio de Janeiro, 1996.