Author(s) :
Haizhong Li,
Udo Simon
Preprint series of the Institute of Mathematics, Technische Universität Berlin
MSC 2000
- 53C42 Immersions
-
53A10 Minimal surfaces, surfaces with prescribed mean curvature
Abstract :
For minimal surfaces in spheres, there is a well known conjecture about
the quantization of intrinsic curvature which has been solved only in special
cases so far. We recall an intrinsic and an extrinsic version for the
known results and extend them to compact non-minimal surfaces in spheres.
In particular we discuss special classes like Willmore surfaces and surfaces with parallel mean curvature vector.
Keywords :
Minimal surfaces in spheres, quantization of curvature, mean curvature vector, Veronese surface, Willmore surface