ON THE PLANE SECTIONS OF THE TANGENT SURFACE OF A SPACE CURVE

<正> 1.Introduction.Let the tangent surface of an analytic curve Cin ordinary space be cut by a plane through a tangent at an ordinarypoint O of C,then the plane section thus obtained has a point of in-flexion at O,provided that the plane is not osculating to C at O.Thisis a well-known fact.Prof.Bompiani has enriched the projectivedifferential geometry of a plane curve at the neighbourhood of a point ofinflexion by introducing various covariant osculants.Prof.Su hasgiven some remarkable properties of the loci of the cusp-tangent t ofthe seven-point cusped cubic of the plane section of the tangent surfacemade by a variable plane n through a tangent of C at O.Prof.Lanehas investigated the loci of the osculants and various points and linesintroduced by Prof.Bompiani.The object of this note is to obtain someproperties of other loci related to the same problem as considered byProf.Su.

ON THE PLANE SECTIONS OF THE TANGENT SURFACE OF A SPACE CURVE