1,720,969 research outputs found
-rigidity of complex hyperbolic manifolds
No full textLet f:(Y,g)→(X,g 0 ) be a nonzero degree continuous map between compact Kähler manifolds of dimension n≥2, where g 0 has constant negative holomorphic sectional curvature. Adapting the Besson–Courtois–Gallot barycentre map techniques to the Kähler setting, we prove a gap theorem in terms of the degree of f and the diastatic entropies of (Y,g) and (X,g 0 ) which extends the rigidity result proved by the author in [13]
Minimal symplectic atlases of Hermitian symmetric spaces
Full text linkIn this paper we estimate the minimal number of Darboux charts needed to cover a Hermitian symmetric space of compact type M in terms of the degree of their embeddings in CPN. The proof is based on the recent work of Rudyak and Schlenk (Commun Contemp Math 9(6):811–855, 2007) and on the symplectic geometry tool developed by the first author in collaboration with Loi et al. (J Sympl Geom, 2014). As application we compute this number for a large class of Hermitian symmetric spaces of compact type
On the Δ -property for complex space forms
No full textInspired by the work of Lu and Tian (Duke Math J 125:351--387, 2004), Loi et al. address in (Abh Math Semin Univ Hambg 90: 99-109, 2020) the problem of studying those Kähler manifolds satisfying the Δ -property, i.e. such that on a neighborhood of each of its points the k-th power of the Kähler Laplacian is a polynomial function of the complex Euclidean Laplacian, for all positive integer k. In particular they conjectured that if a Kähler manifold satisfies the Δ -property then it is a complex space form. This paper is dedicated to the proof of the validity of this conjecture
Diastatic entropy and rigidity of complex hyperbolic manifolds
No full textLet f : Y → X be a continuous map between a compact real analytic Kähler manifold (Y, g) and a
compact complex hyperbolic manifold (X, g0). In this paper we give a lower bound of the diastatic entropy
of (Y, g) in terms of the diastatic entropy of (X, g0) and the degree of f . When the lower bound is attained
we get geometric rigidity theorems for the diastatic entropy analogous to the ones obtained by G. Besson, G.
Courtois and S. Gallot [2] for the volume entropy. As a corollary,when X = Y,we get that the minimal diastatic
entropy is achieved if and only if g is isometric to the hyperbolic metric g0
KÄhler immersions of KÄhler-Ricci solitons into definite or indefinite complex space forms
Full text linkLet (g, X) be a Kähler-Ricci soliton (KRS) on a complex manifold M. We prove that if the Kähler manifold (M, g) can be Kähler immersed into a definite or indefinite complex space form then g is Einstein. Notice that there is no topological assumptions on the manifold M and the Kähler immersion is not required to be injective. Our result extends the result obtained in Bedulli and Gori [Proc. Amer. Math. Soc. 142 (2014), pp. 1777-1781] asserting that a KRS on a compact Kähler submanifold M ⊂ CPN which is a complete intersection is Kähler-Einstein (KE)
Immersions of Sasaki–Ricci solitons into homogeneous Sasakian manifolds
Full text linkWe discuss local Sasakian immersion of Sasaki-Ricci solitons (SRS) into fiber products of homogeneous Sasakian manifolds. In particular, we prove that SRS locally induced by alarge class of fiber products of homogeneous Sasakian manifolds are, in fact, eta-Einstein. The results are stronger for immersions into Sasakian space forms. Moreover, we show an example of a Kähler-Ricci soliton on C^n which admits no local holomorphic isometry into products of homogeneous bounded domains with flat Kähler manifolds and generalized flag manifolds
Symplectic capacities of hermitian symmetric spaces of compact and noncompact type
No full textInspired by the work of G. Lu on pseudo symplectic capacities we obtain several results on the Gromov width and the Hofer-Zehnder capacity of Hermitian symmetric spaces of compact type. Our results and proofs extend those obtained by Lu for complex Grassmannians to Hermitian symmetric spaces of compact type. We also compute the Gromov width and the Hofer-Zehnder capacity for Cartan domains and their products
Some remarks on Homogeneous Kaehler manifolds
No full textIn this paper we provide a positive answer to a conjecture due to Di Scala et al. (Asian J Math, 2012, Conjecture 1) claiming that a simply-connected homogeneous Kähler manifold M endowed with an integral Kähler form μ0ω, admits a holomorphic isometric immersion in the complex projective space, for a suitable >0μ0>0. This result has two corollaries which extend to homogeneous Kähler manifolds the results obtained by the authors Loi and Mossa (Geom Dedicata 161:119–128, 2012) and Mossa (J Geom Phys 86:492–496, 2014) for homogeneous bounded domains
- …
