Complete bounded null curves immersed in C^3 and SL(2,C)

Details Complete bounded null curves immersed in C^3 and SL(2,C) Complete bounded null curves immersed in C^3 and SL(2,C)

2006-03-22

arxiv.org/abs/math/0603530v6

Mathematics

Differential Geometry

24 pages, 6 figures. To appear in Calculus of Variantions and P.D.E.'s

Scientific paper

We construct a simply connected complete bounded Bryant surface in the hyperbolic 3-space H^3. Such a surface in H^3 can be lifted as a complete bounded null curve in SL(2,C). Using a transformation between null curves in C^3 and null curves in SL(2,C), we are able to produce the first examples of complete bounded null curves in C^3. As an application, we can show the existence of a complete bounded minimal surface in R^3 whose conjugate minimal surfaces are all bounded. Moreover, we can show the existence of a complete bounded immersed complex submanifold in C^2.

Affiliated with

Also associated with

No associations

Rating

Complete bounded null curves immersed in C^3 and SL(2,C) 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 Complete bounded null curves immersed in C^3 and SL(2,C), we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Complete bounded null curves immersed in C^3 and SL(2,C) will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-548691