View source for Demoulin surface

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A surface formed by a conjugate net of lines the tangents to which form two $W$-congruences — a so-called singular conjugate system. Only the Demoulin surfaces permit a [[Projective deformation|projective deformation]]. Introduced by A. Demoulin .

====References====
<table><TR><TD valign="top">[1a]</TD> <TD valign="top">  A. Demoulin,   "Sur les surfaces $R$ et les surfaces $\Omega$"  ''C.R. Acad. Sci. Paris'' , '''153'''  (1911)  pp. 590–593</TD></TR><TR><TD valign="top">[1b]</TD> <TD valign="top">  A. Demoulin,   "Sur les surfaces $R$ et les surfaces $\Omega$"  ''C.R. Acad. Sci. Paris'' , '''153'''  (1911)  pp. 705–707</TD></TR><TR><TD valign="top">[1c]</TD> <TD valign="top">  A. Demoulin,   "Sur les surfaces $R$"  ''C.R. Acad. Sci. Paris'' , '''153'''  (1911)  pp. 797–799</TD></TR><TR><TD valign="top">[1d]</TD> <TD valign="top">  A. Demoulin,   "Sur les surfaces $\Omega$"  ''C.R. Acad. Sci. Paris'' , '''153'''  (1911)  pp. 927–929</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  S.P. Finikov,   "Projective-differential geometry" , Moscow-Leningrad  (1937)  (In Russian)</TD></TR><TR><TD valign="top">[3]</TD> <TD valign="top">  A.P. Norden,   "Spaces with an affine connection" , Nauka , Moscow-Leningrad  (1976)  (In Russian)</TD></TR></table>



====Comments====
The terminology concerned with Demoulin surfaces differs. In [[#References|[a1]]] they are roughly characterized by the fact that the Demoulin tetrahedron (see [[Demoulin quadrilateral|Demoulin quadrilateral]]) degenerates to one point. The existence of a projective deformation is a more general condition (see [[#References|[a1]]], Par. 119) The problem of projective deformation is related to $R$-congruences, which are special $W$-congruences (see [[#References|[a1]]] and [[#References|[2]]], [[#References|[3]]]).

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  G. Bol,   "Projective Differentialgeometrie" , '''2''' , Vandenhoeck &amp; Ruprecht  (1954)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  E.P. Lane,   "A treatise on projective differential geometry" , Univ. Chicago Press  (1942)</TD></TR></table>