Summary
The aim of this paper is to determine rectilinear congruences in the Euclidean space of three dimension whose straight lines preserve the Gauss curvature of their focal surfaces.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L. Bianchi,Lezioni di Geometria differenziate, Zanichelli, Bologna, 1927.
L. Bianchi,Vorlesüngen über Differentialgeometrie, Zweite Auflage, Teubner, 1927.
L.Eisenhart,Riemannian Geometry, Princeton University Press, 1964.
S. Finikoff,Congruences avec les deux nappes de la surface focale applicables l'une sur l'autre par les points correspondants, Annali di Mat.,41 (1924), pp. 175–180.
Van K. Kommerel,Theorie der Raumkurven and krummen Flächen, de Gruyter, 1–2 Band, Berlin, 1931.
O. Pylarinos,Sur certains réseaux de courbes tracés sur une surface, Bull. Sc. Math. 2e,84 (1960), pp. 116–144.
O. Pylaeinos,Sur les surfaces à courbure moyenne constante applicable sur des surfaces de revolution, Annali di Matematica pura ed applicata, (IV),59 (1962), pp. 319–350.
Gr. Tsagas,Two special categories of normal rectilinear congruences, Bull. de la Soc. Math., Grèce,7 (1966), pp. 161–172.
Gr. Tsagas,Sur deux classes particulières de congruences de normales, C. R. Acad. Sci. Paris,263 (1966), pp. 407–409.
Gr. Tsagas,On the rectilinear congruence whose straight lines are tangent to one parameter family of curves on a surface, Tensor N.S.,29 (1975), pp. 287–294.
Gr. Tsagas,On the surfaces whose normal bundles have special properties, Bull. de la Soc. Math., Grèce,15 (1974), pp. 59–67.
Gr.Tsagas - B.Papantoniou,Special class or rectilinear congruences, to appear Mathematica Balkanika.
Gr.Tsagas - B.Papantoniou,On the rectilinear congruences of Lorentz manifold establishing an area preserving representation, to appear Tensor N.S.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Tsagas, G., Papantoniou, B. On the rectilinear congruences establishing a mapping between its focal surfaces which preserves the Gauss curvature. Annali di Matematica pura ed applicata 131, 255–264 (1982). https://doi.org/10.1007/BF01765155
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01765155