Gauss curvature

Value distribution theory of the Gauss map of complete regular minimal surfaces has a long history, in particular, much attention has been given to this theory from the viewpoint of the Nevanlinna theory. In this article, we will establish an estimate for the Gaussian curvature of minimal surfaces in R 4 whose classical Gauss map is ramified over the set of distinct points.

12p visharma 20-10-2023 3 2   Download

The structure of pointwise slant submanifolds in an almost product Riemannian manifold is investigated and the special proper pointwise slant surfaces of a locally product manifold are introduced. A relation involving the squared mean curvature and the Gauss curvature of pointwise slant surface of a locally product manifold is proved.

16p danhdanh27 07-01-2019 10 2   Download

An important problem in conformal geometry is the construction of conformal metrics for which a certain curvature quantity equals a prescribed function, e.g. a constant. In two dimensions, the uniformization theorem assures the existence of a conformal metric with constant Gauss curvature. Moreover, J. Moser [20] proved that for every positive function f on S 2 satisfying f (x) = f (−x) for all x ∈ S 2 there exists a conformal metric on S 2 whose Gauss curvature is equal to f . A natural conformal invariant in dimension four is 1 Q = − (∆R −...

22p tuanloccuoi 04-01-2013 46 6   Download