Geometry of Projective Planes over Two-Dimensional Algebras

Details Geometry of Projective Planes over Two-Dimensional Algebras Geometry of Projective Planes over Two-Dimensional Algebras

2000-10-19

arxiv.org/abs/math/0010192v1

Beitraege Algebra Geom., 44 (2003) no. 1 165-178

Mathematics

Differential Geometry

AMS-LaTeX, 11 pages

Scientific paper

The authors study smooth lines on projective planes over the algebra C of complex numbers, the algebra C^1 of double numbers, and the algebra C^0 of dual numbers. In the space RP^5, to these smooth lines there correspond families of straight lines describing point three-dimensional tangentially degenerate submanifolds X^3 of rank 2. The authors study focal properties of these submanifolds and prove that they represent examples of different types of tangentially degenerate submanifolds. Namely, the submanifold X^3, corresponding in RP^5 to a smooth line \gamma of the projective plane C, does not have real singular points, the submanifold X^3, corresponding in RP^5 to a smooth line \gamma of the projective plane C^1 P^2, bears two plane singular lines, and finally the submanifold X^3, corresponding in RP^5 to a smooth line \gamma of the projective plane C^0 P^2, bears one singular line.

Affiliated with

Also associated with

No associations

Rating

Geometry of Projective Planes over Two-Dimensional Algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Geometry of Projective Planes over Two-Dimensional Algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometry of Projective Planes over Two-Dimensional Algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-397397