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 Joyces
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.
·
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.
·
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.
·
Projective homogeneity, manuscripta
math. 64 (1989) p. 155-167
·
A class of symmetric spaces, Bull. Soc. Math.
· 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)