7,949 research outputs found
On the Spinor Representation of Surfaces in Euclidean 3-Space
The aim of the present paper is to clarify the relationship between
immersions of surfaces and solutions of the inhomogeneous Dirac equation. The
main idea leading to the description of a surface M^2 by a spinor field is the
observation that the restriction to M^2 of any parallel spinor phi on R^3 is
(with respect to the inner geometry of M^2) a non-trivial spinor field on M^2
of constant length which is a solution of the inhomogeneous Dirac equation and
vice versa.Comment: 16 pages, LaTeX2.0
Spin(9)-structures and connections with totally skew-symmetric torsion
We study Spin(9)-structures on 16-dimensional Riemannian manifolds and
characterize the geometric types admitting a connection with totally
skew-symmetric torsion.Comment: Latex2e, 8 page
Eigenvalue estimates for the Dirac operator depending on the Weyl curvature tensor
We prove new lower bounds for the first eigenvalue of the Dirac operator on
compact manifolds whose Weyl tensor or curvature tensor, respectively, is
divergence free. In the special case of Einstein manifolds, we obtain estimates
depending on the Weyl tensor.Comment: Latex2.09, 9 page
The Casimir operator of a metric connection with skew-symmetric torsion
For any triple consisting of a Riemannian manifold and a
metric connection with skew-symmetric torsion we introduce an elliptic, second
order operator acting on spinor fields. In case of a reductive space
and its canonical connection our construction yields the Casimir operator of
the isometry group. Several non-homogeneous geometries (Sasakian, nearly
K\"ahler, cocalibrated -structures) admit unique connections with
skew-symmetric torsion. We study the corresponding Casimir operator and compare
its kernel with the space of -parallel spinors.Comment: Latex2e, 15 page
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