The Codazzi Equation for Surfaces

Details The Codazzi Equation for Surfaces The Codazzi Equation for Surfaces

2009-02-13

arxiv.org/abs/0902.2283v1

Mathematics

Differential Geometry

Scientific paper

In this paper we develop an abstract theory for the Codazzi equation on surfaces, and use it as an analytic tool to derive new global results for surfaces in the space forms ${\bb R}^3$, ${\bb S}^3$ and ${\bb H}^3$. We give essentially sharp generalizations of some classical theorems of surface theory that mainly depend on the Codazzi equation, and we apply them to the study of Weingarten surfaces in space forms. In particular, we study existence of holomorphic quadratic differentials, uniqueness of immersed spheres in geometric problems, height estimates, and the geometry and uniqueness of complete or properly embedded Weingarten surfaces.

Affiliated with

Also associated with

No associations

Rating

The Codazzi Equation for Surfaces 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 The Codazzi Equation for Surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Codazzi Equation for Surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-357212