Deformations of nearly Kähler instantons

We formulate the deformation theory for instantons on nearly Kähler six-manifolds using spinors and Dirac operators. Using this framework we identify the space of deformations of an irreducible instanton with semisimple structure group with the kernel of an elliptic operator, and prove that abelian instantons are rigid. As an application, we show that the canonical connection on three of the four homogeneous nearly Kähler six-manifolds G/H is a rigid instanton with structure group H. In contrast, these connections admit large spaces of deformations when regarded as instantons on the tangent bundle with structure group SU(3)

Zoneamento Agroecológico do município de Ponta Porã/MS.

bitstream/item/25433/1/bpd137-2009-ponta-pora-ms.pd

STRUCTURE THEOREMS FOR CONSTANT MEAN-CURVATURE SURFACES BOUNDED BY A PLANAR CURVE

Introduction A circle C in R 3 is the boundary of two spherical caps of constant mean curvature H for any positive number H, which is at most the radius of C. It is natural to ask whether spherical caps are the only possible examples. Some examples of constant mean curvature immersed tori by Wente [7] indicate that there are compact genus-one immersed constant mean curvature surfaces with boundary C that are approximated by compact domains in Wente tori; however, this has not been proved. Still one has the conjecture: Conjecture 1 A compact constant mean curvature surface bounded by a circle is a spherical cap if either of the following conditions hold: 1. The surface has genus 0 and is immersed; 2. The surface is embedded. If M is a compact embedded constant mean curvature surface in R 3 with boundary C<F1