Attività Scientifica/ Research.

Interessi di ricerca: mi occupo di vari argomenti di geometria differenziale, con particolare interesse all'azione di gruppi (di Lie, algebrici) su varietà. Di particolare interesse sono le azioni di gruppi di Lie compatti (o algebrici riduttivi) su varietà Kähler (varietà affini), con particolare riguardo alle azioni multiplicity- free, alla natura delle orbite, alla mappa momento; un ulteriore campo di ricerca, pure legato all'azione di gruppi di Lie, è costituito dalla ricerca di metriche di Kähler-Einstein su varietà Kähler compatte dotate di un ampio gruppo di isometrie.

Research interests: I am working in the field of differential geometry, with particular interest for actions of Lie (algebraic) groups on manifolds (varieties). I am mainly interested in the Lie (algebraic) group actions on Kähler (affine) manifolds, in particular in multiplicity-free actions, the geometric structure of the orbits, the moment map; I am also studying new  Kähler-Einstein metrics on compact Kähler manifolds which are acted on by a large isometry group.

Sono reviewer per l'American Mathematical Society

Lista delle pubblicazioni/ Publications

· On the first eigenvalue of invariant Kaehler metrics, con F. Panelli, axiv (2014)

· The index of symmetry of a flag manifold , to appear in Rev. Mat. Iberoam.

· Tight Lagrangian homology spheres in compact homogeneous Kaehler manifolds, con C. Gorodski, arXiv:1308.3670 (2013), to appear in Israel Journal of Math.

· On moduli spaces of Ricci solitons, con A. Spiro, J. Geom. Anal. 25 (2015), 1157-1174

· Six-dimensional nearly Kaehler manifolds of cohomogeneity one (II), con A. Spiro, Comm. Math. Phys. 312 (2012), 477-500

· Homogeneous Hypercomplex manifolds and the Joyce’s examples, con L.Bedulli e A. Gori, Differential Geom. And its Appl.29 (2011), 547-554

· Construction of Lagrangian submanifolds of CP^n and Hamiltonian stability, con D. Petrecca, Tohoku Math. J. (2012)

· Six-dimensional nearly Kaehler manifolds of cohomogeneity one, con A. Spiro, J. Geom. Phys. 60 (2010), 156-164

· Maximal totally complex submanifolds of HPⁿ: homogeneity and normal holonomy , con L. Bedulli, A. Gori , Bull London Math. Soc. 41 (2009), 1029-1040

· Kähler-Ricci solitons on homogeneous toric bundles, with A. Spiro , in Crelles J. (2009)

· A note on moment maps and Kähler-Einstein manifolds, Int. J. Geom. Methods Mod, Phys. (2006) 1215-1219

· Cohomogeneity one hypersurfaces of Euclidean spaces, with F. Mercuri, Seixas J.A.P., Tojeiro R. , Comment. Math. Helv. 81 (2006), 471- 489 

· Homogeneous toric bundles with positive first Chern class, with A. Spiro, preprint (2004)

· Complex Asystatic actions of compact Lie groups, with A. Gori, Transformation Groups 11 (2006) 177-184

· A note on the moment map on compact Kähler manifolds, with A. Gori, Annals Global Analysis and Geom. 26 (3)  (2004) 315-318

· Homogeneity rank of real representations of compact Lie groups, with C. Gorodski, to appear in Journal of Lie Theory (2004)

· Two-orbit Kähler manifolds and Morse Theory, with A. Gori, Monatshefte für Math. 143 (2) (2004) 105-114

· Homogeneous spaces with polar isotropy, with A. Kollross, manuscripta math. 110 (2003) 487-503.

· Coisotropic actions on compact homogeneous Kähler manifolds, with G. Thorbergsson,  Math. Z. 243 (2002) 471-490

· Polar and coisotropic actions on Kähler manifolds, with G. Thorbergsson, Trans. A.M.S. 354 (2002), p. 1759-1781

· New examples of Kähler-Einstein almost homogeneous manifolds, with A. Spiro, Indiana Univ. Math. J. 52 (2003) 1027-1074

· A note on quaternion-Kähler manifolds, with L. Verdiani, Int. J. Math. 11 (2000), p. 279-283

· Polar actions on rank-one symmetric spaces, with G. Thorbergsson, J. Diff. Geom. 53 (1999), p. 131-175

· Kähler manifolds with large isometry group, with A. Spiro, Osaka J. Math. 36 (1999), p. 805-833

· Positively curved 7-dimensional manifolds, with L. Verdiani, Quart. J. Math. Oxford 50 (1999), p. 497-504

· Totally geodesic orbits of isometries, with L. Verdiani, Ann. Global Anal.Geom. 16 (1998), p. 399-412

· Compact cohomogeneity one Riemannian manifolds of positive Euler characteristic and quaternionic Kaehler manifolds, with  D.V. Alekseevsky, in Geometry, Topology and Physics, Eds. Apanasov,Bradlow,Rodrigues,Uhlenbeck, Walter de Gruyter (1997), p. 1-33

· Some remarks on austere submanifolds, Boll. U.M.I. 11-B (1997), p. 157-160

· A fixed point theorem, Arch. Math. 68 (1997), p. 65-69

· Immersions of cohomogeneity one manifolds, Monatshefte für  Math. 172 (1996), p. 215-225

· Some topological properties of cohomogeneity one manifolds with negative curvature, with A. Spiro, Ann. Global Anal. Geom. 14 (1996), p. 69-79

· Cohomogeneity one manifolds and hypersurfaces of revolution, with A. Spiro, Ann. Global Anal.  Geom. 13 (1995), p. 169-184

· Four-dimensional Einstein-like manifolds and curvature homogeneity, with A. Spiro, Geometriae Dedicata 54 (1995), p. 225-243

· A canonical connection for Lie group actions, Results in Math. 27 (1995), p. 105-112

· Cohomogeneity one Riemannian manifolds and Killing fields, Diff. Geom. And its Appl. 5 (1995), p. 311-320

· Riemannian manifolds with special curvature tensor, with F.Tricerri, Rend. Ist. Mat. Univ. Trieste XXVI (1994), p. 95-101

· Projectively flat surfaces in A³, Proc. A.M.S. 119 (1993), p.255-260

· Automorphisms of hyperbolic domains in Rⁿ, Geometriae Dedicata 42 (1992), p. 317-327

· Isometries of tangent sphere bundles, Boll. U.M.I. 7 (1991), p. 207-214

· Affine Kähler hypersurfaces satisfying certain conditions on the curvature tensor, Results in Math. 19 (1991), p. 147-156

· On the Cartan-Norden theorem for affine Kähler immersions, with K. Nomizu, Nagoya Math. J. 121 (1991), p. 127-135

· Projective submersions, Bulletin Australian Math. Soc. 43 (1991), 251-256

· On the geometry of affine Kähler immersions, with K. Nomizu, Nagoya Math. J. 120 (1990), p. 205-222

· Projective structures on reductive homogeneous spaces, Proc. A.M.S. 109 (1990), p.1087-1096

· On affine Kähler structures, with K. Nomizu, Bull. Soc. Math. Belg. 41 (1989), p. 275-282

· Projective hyperbolicity, Quart. J. Math. Oxford 40 (1989), p. 325-331

· Projective homogeneity, manuscripta math. 64 (1989) p. 155-167

· A class of symmetric spaces, Bull. Soc. Math. France 117 (1989) p. 343-360

· Projectively symmetric spaces, Ann. Matematica Pura e Appl., CLIV (1989), p. 371-383

· Projective invariant metrics and open convex regular cones I, II, Atti Acc.Lincei Rend. Fis. LXXXI (1987),  p. 125-137 and 139-147

Libri

· Lezioni di geometria differenziale, con G. Gentili, E. Vesentini Bollati-Boringhieri (1995)