The Energy-Momentum tensor on $Spi{n}^c$ manifolds

Abstract

On $Spi{n}^c$ manifolds, we study the Energy-Momentum tensor associated with a spinor field. First, we give a spinorial Gauss type formula for oriented hypersurfaces of a $Spi{n}^c$ manifold. Using the notion of generalized cylinders, we derive the variationnal formula for the Dirac operator under metric deformation and point out that the Energy-Momentum tensor appears naturally as the second fundamental form of an isometric immersion. Finally, we show that generalized $Spi{n}^c$ Killing spinors for Codazzi Energy-Momentum tensor are restrictions of parallel spinors.

To appear in IJGMMP (International Journal of Geometric Methods in Modern Physics), 22 pages

References in corpus (3)

• Generalized Cylinders in Semi-Riemannian and Spin Geometry
• Energy-Momentum tensor on foliations
• Lower Bounds for the Eigenvalues of the Dirac Operator on $Spi{n}^c$ Manifolds

Cited by in corpus (6)

• Lower Bounds for the Eigenvalues of the Dirac Operator on $Spi{n}^c$ Manifolds
• Spinorial Representation of Submanifolds in Riemannian Space Forms
• Boundary value problems for noncompact boundaries of Spin${}^c$ manifolds and spectral estimates
• The Spin${}^c$ Dirac Operator on Hypersurfaces and Applications
• Characterization of hypersurfaces in four dimensional product spaces via two different Spin${}^c$ structures
• Spinorial Characterization of CR Structures, I