Lower bounds for the eigenvalues of the basic Dirac operator. (English) Zbl 1104.53024

Slovák, Jan (ed.) et al., The proceedings of the 24th winter school “Geometry and physics”, Srní, Czech Republic, January 17–24, 2004. Palermo: Circolo Matemático di Palermo. Supplemento ai Rendiconti del Circolo Matemático di Palermo. Serie II 75, 241-250 (2005).
This is a brief survey article on the eigenvalue estimates of the basic Dirac operator on the Riemannian manifold with the transverse spin foliation based on author’s papers [J. Geom. Phys. 39, No. 3, 253–264 (2001; Zbl 1024.53019), J. Geom. Phys. 45, No. 1–2, 75–90 (2003; Zbl 1027.53051) and J. Geom. Phys. 51, No. 2, 166–182 (2004; Zbl 1076.58022)].
For the entire collection see [Zbl 1074.53001].


53C12 Foliations (differential geometric aspects)
53C27 Spin and Spin\({}^c\) geometry
57R30 Foliations in differential topology; geometric theory