About Twistor Spinors with Zero in Lorentzian Geometry TeX Export

@article{citeulike:5305927, abstract = {We describe the local conformal geometry of a Lorentzian spin manifold \$(M,g)\$ admitting a twistor spinor \$\phi\$ with zero. Moreover, we describe the shape of the zero set of \$\phi\$. If \$\phi\$ has isolated zeros then the metric \$g\$ is locally conformally equivalent to a static monopole. In the other case the zero set consists of null geodesic(s) and \$g\$ is locally conformally equivalent to a Brinkmann metric. Our arguments utilise tractor calculus in an essential way. The Dirac current of \$\phi\$, which is a conformal Killing vector field, plays an important role for our discussion as well.}, archivePrefix = {arXiv}, author = {Leitner, Felipe}, citeulike-article-id = {5305927}, citeulike-linkout-0 = {http://arxiv.org/abs/math/0406298}, citeulike-linkout-1 = {http://arxiv.org/pdf/math/0406298}, day = {28}, eprint = {math/0406298}, keywords = {lorentzian-geometry, math, spinor, twistors}, month = {Jul}, posted-at = {2009-07-30 21:31:57}, priority = {2}, title = {About Twistor Spinors with Zero in Lorentzian Geometry}, url = {http://arxiv.org/abs/math/0406298}, year = {2009} }

TY - JOUR ID - citeulike:5305927 L3 - citeulike-article-id:5305927 N2 - We describe the local conformal geometry of a Lorentzian spin manifold $(M,g)$ admitting a twistor spinor $\phi$ with zero. Moreover, we describe the shape of the zero set of $\phi$. If $\phi$ has isolated zeros then the metric $g$ is locally conformally equivalent to a static monopole. In the other case the zero set consists of null geodesic(s) and $g$ is locally conformally equivalent to a Brinkmann metric. Our arguments utilise tractor calculus in an essential way. The Dirac current of $\phi$, which is a conformal Killing vector field, plays an important role for our discussion as well. TI - About Twistor Spinors with Zero in Lorentzian Geometry KW - lorentzian-geometry KW - math KW - spinor KW - twistors AU - Leitner, Felipe PY - 2009/Jul/28/ UR - http://arxiv.org/abs/math/0406298 ER -