@article {2011, title = {Holomorphic Cartan geometry on manifolds with numerically effective tangent bundle}, journal = {Differential Geometry and its Applications 29 (2011) 147-153}, number = {SISSA;05/2010/FM}, year = {2011}, publisher = {Elsevier}, doi = {10.1016/j.difgeo.2011.02.001}, url = {http://hdl.handle.net/1963/3830}, author = {Indranil Biswas and Ugo Bruzzo} } @article {2010, title = {On semistable principal bundles over complex projective manifolds, II}, journal = {Geom. Dedicata 146 (2010) 27-41}, number = {SISSA;85/2008/FM}, year = {2010}, abstract = {Let (X, \\\\omega) be a compact connected Kaehler manifold of complex dimension d and E_G a holomorphic principal G-bundle on X, where G is a connected reductive linear algebraic group defined over C. Let Z (G) denote the center of G. We prove that the following three statements are equivalent: (1) There is a parabolic subgroup P of G and a holomorphic reduction of the structure group of E_G to P (say, E_P) such that the bundle obtained by extending the structure group of E_P to L(P)/Z(G) (where L(P) is the Levi quotient of P) admits a flat connection; (2) The adjoint vector bundle ad(E_G) is numerically flat; (3) The principal G-bundle E_G is pseudostable, and the degree of the charateristic class c_2(ad(E_G) is zero.}, doi = {10.1007/s10711-009-9424-8}, url = {http://hdl.handle.net/1963/3404}, author = {Indranil Biswas and Ugo Bruzzo} } @article {2008, title = {On semistable principal bundles over a complex projective manifold}, journal = {Int. Math. Res. Not. vol. 2008, article ID rnn035}, number = {arXiv.org;0803.4042v1}, year = {2008}, publisher = {Oxford University Press}, abstract = {Let G be a simple linear algebraic group defined over the complex numbers. Fix a proper parabolic subgroup P of G and a nontrivial antidominant character \\\\chi of P. We prove that a holomorphic principal G-bundle E over a connected complex projective manifold M is semistable and the second Chern class of its adjoint bundle vanishes in rational cohomology if and only if the line bundle over E/P defined by \\\\chi is numerically effective. Similar results remain valid for principal bundles with a reductive linear algebraic group as the structure group. These generalize an earlier work of Y. Miyaoka where he gave a characterization of semistable vector bundles over a smooth projective curve. Using these characterizations one can also produce similar criteria for the semistability of parabolic principal bundles over a compact Riemann surface.}, doi = {10.1093/imrn/rnn035}, url = {http://hdl.handle.net/1963/3418}, author = {Indranil Biswas and Ugo Bruzzo} }