Resitel se seznami jednak se symplektickou konexi na symplektickych varietach (fazove prostory klasicke mechaniky) pripoustejicich metaplektickou strukturu a s rovnici pro symplekticky Killinguv spinor, jednak take s riemannovskymi verzemi predchozich pojmu. Zjisti existenci symplektickych Killingovych spinoru na jednoduchych prikladech variet s metaplektickou strukturou (sfera, vektorovy prostor sude dimenze) nebo ukaze souvislosti spekter operatoru pro vyssi symplekticky spin v souvislosti se symplektickymi twistorovymi operatory.
References
[1] Habermann, K., Habermann, L.: Introduction to symplectic Dirac operators, Springer, Berlin-Heidelberg-New York, 2006.
[2] Krysl, S.: Spectral properties of symplectic Dirac and Rarita-Schwinger operators, to appear in Arch. Math. (Brno), 2008; zatim preprint.
[3] Friedrich, T.: Dirac operators in Riemannian geometry, AMS, Providence, Rhode Island, 2000.
Preliminary scope of work
V riemannovske geometrii existence Killingovych spinoru imlikuje silne geometricke restrikce (einsteinovskost) na varietu, na niz jsou Killingovy spinory zkoumany. Bude zkoumana analogicka situace v pripade symplektickych variet s metaplektickou strukturou.
Preliminary scope of work in English
In Riemannian geometry, the existence of Killing spinors implies strict restrictions on the geometry (einsteinity) of the studied manifold. A parallel situation to the Riemannian case will be studied, in the realm of symplectic manifolds admitting a metaplectic structure.
