Displaying similar documents to “On the Gaussian and mean curvature of certain surfaces.”

Complete classification of spatial surfaces with parallel mean curvature vector in arbitrary non-flat pseudo-Riemannian space forms

Bang-Yen Chen (2009)

Open Mathematics

Similarity:

Submanifolds with parallel mean curvature vector play important roles in differential geometry, theory of harmonic maps as well as in physics. Spatial surfaces in 4D Lorentzian space forms with parallel mean curvature vector were classified by B. Y. Chen and J. Van der Veken in [9]. Recently, spatial surfaces with parallel mean curvature vector in arbitrary pseudo-Euclidean spaces are also classified in [7]. In this article, we classify spatial surfaces with parallel mean curvature vector...

The PDE describing constant mean curvature surfaces

Hongyou Wu (2001)

Mathematica Bohemica

Similarity:

We give an expository account of a Weierstrass type representation of the non-zero constant mean curvature surfaces in space and discuss the meaning of the representation from the point of view of partial differential equations.

Invariants and Bonnet-type theorem for surfaces in ℝ4

Georgi Ganchev, Velichka Milousheva (2010)

Open Mathematics

Similarity:

In the tangent plane at any point of a surface in the four-dimensional Euclidean space we consider an invariant linear map ofWeingarten-type and find a geometrically determined moving frame field. Writing derivative formulas of Frenet-type for this frame field, we obtain eight invariant functions. We prove a fundamental theorem of Bonnet-type, stating that these eight invariants under some natural conditions determine the surface up to a motion. We show that the basic geometric classes...