%0 Journal Article %J Differential Geometry and its Applications 29 (2011) 147-153 %D 2011 %T Holomorphic Cartan geometry on manifolds with numerically effective tangent bundle %A Indranil Biswas %A Ugo Bruzzo %B Differential Geometry and its Applications 29 (2011) 147-153 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3830 %1 497 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-01-26T15:20:25Z\\r\\nNo. of bitstreams: 1\\r\\nbiswas-bruzzo_2010.pdf: 181667 bytes, checksum: ac09c3a64c7a8642ae63e2b807f2da64 (MD5) %R 10.1016/j.difgeo.2011.02.001 %0 Journal Article %J Geom. Dedicata 146 (2010) 27-41 %D 2010 %T On semistable principal bundles over complex projective manifolds, II %A Indranil Biswas %A Ugo Bruzzo %X 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. %B Geom. Dedicata 146 (2010) 27-41 %G en_US %U http://hdl.handle.net/1963/3404 %1 928 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-12-31T11:15:29Z\\nNo. of bitstreams: 1\\nbiswas-bruzzo-2.pdf: 216946 bytes, checksum: 21a4d096140b009d34e486648fe1a555 (MD5) %R 10.1007/s10711-009-9424-8 %0 Journal Article %J Int. Math. Res. Not. vol. 2008, article ID rnn035 %D 2008 %T On semistable principal bundles over a complex projective manifold %A Indranil Biswas %A Ugo Bruzzo %X 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. %B Int. Math. Res. Not. vol. 2008, article ID rnn035 %I Oxford University Press %G en_US %U http://hdl.handle.net/1963/3418 %1 917 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-01-12T09:53:34Z\\nNo. of bitstreams: 1\\n0803.4042v1.pdf: 273878 bytes, checksum: 8f729aa65d9cebf234016c17cacfedbc (MD5) %R 10.1093/imrn/rnn035