On the Spinor Representation of Surfaces in Euclidean

On the Spinor Representation of Surfaces in Euclidean 3-space. *

Characterizations of Slant Ruled Surfaces in the Euclidean 3-space

In this study, we give the relationships between the conical curvatures of ruled surfaces generated by the unit vectors of the ruling, central normal and central tangent of a ruled surface in the Euclidean 3-space E^3. We obtain differential equations characterizing slant ruled surfaces and if the reference ruled surface is a slant ruled surface, we give the conditions for the surfaces generate...

The Spinor Representation of Minimal Surfaces

The spinor representation is developed and used to investigate minimal surfaces in R with embedded planar ends. The moduli spaces of planar-ended minimal spheres and real projective planes are determined, and new families of minimal tori and Klein bottles are given. These surfaces compactify in S to yield surfaces critical for the Möbius invariant squared mean curvature functional W . On the ot...

Clifford Fourier Transform and Spinor Rep- resentation of Images

We propose in this paper to introduce a spinor representation for images based on the work of T. Friedrich. This spinor representation generalizes to arbitrary surfaces (immersed in R) the usual Weierstrass representation of minimal surfaces (i.e. surfaces with constant mean curvature equal to zero). We investigate applications to image processing focusing on segmentation and Clifford Fourier a...

Surfaces in S3 and H3 via Spinors

We generalize the spinorial characterization of isometric immersions of surfaces in R given by T. Friedrich to surfaces in S and H. The main argument is the interpretation of the energy-momentum tensor associated with a special spinor field as a second fundamental form. It turns out that such a characterization of isometric immersions in terms of a special section of the spinor bundle also hold...