Some remarks on the Gromov width of homogeneous Hodge manifolds

Loi, Andrea; Mossa, Roberto; Zuddas, Fabio

doi:10.1142/s0219887814600299

Cited by 5 publications

(5 citation statements)

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“…By Darboux's theorem c G (M, ω) is a positive number or ∞. Computations and estimates of the Gromov width for various examples can be found in [2,3,4,5,7,8,10,11,14,15,16,17,18,19,21,24]. We adopt the following notation from [14].…”

Section: Introduction and Statements Of The Main Resultsmentioning

confidence: 99%

Minimal symplectic atlases of Hermitian symmetric spaces

Mossa

Placini

2015

Abh. Math. Semin. Univ. Hambg.

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In this paper we compute the minimal number of Darboux chart needed to cover a Hermitian symmetric space of compact type in terms of the degree of their embeddings in $\mathbb{C} P^N$. The proof is based on the recent work of Y. B. Rudyak and F. Schlenk [18] and on the symplectic geometry tool developed by the first author in collaboration with A. Loi and F. Zuddas [12]. As application we compute this number for a large class of Hermitian symmetric spaces of compact type.Comment: 8 page

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Section: Introduction and Statements Of The Main Resultsmentioning

confidence: 99%

Minimal symplectic atlases of Hermitian symmetric spaces

Mossa

Placini

2015

Abh. Math. Semin. Univ. Hambg.

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“…The upper bound c G (M, ω) ≤ π is Theorem 1 in [6]. In order to obtain the lower bound c G (M, ω) ≥ π, consider the integral Kähler form ω = ω π on M. Let (L, h) be the holomorphic hermitian line bundle on M such that Ric(h) = ω, where Ric(h) is the 2-form on M defined by Ric(h) = − i 2π ∂ ∂ log h(σ, σ), for a local trivializing holomorphic section σ of L. Let s 0 , .…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…Computations and estimates of the Gromov width for various examples have been obtained by several authors (see, e.g. [6] and references therein). The main result of this paper is the following theorem proved in the next section.…”

Section: Introductionmentioning

confidence: 99%

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On the Gromov width of homogeneous Kähler manifolds

Loi

Zuddas

2016

Differential Geometry and its Applications

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For generic r = (r1,. .. , rn) ∈ R n + the space M(r) of n-gons in R 3 with edges of lengths r is a smooth, symplectic manifold. We investigate its Gromov width and prove that the expression 2π min{2rj , (i =j ri) − rj | j = 1,. .. , n} is the Gromov width of all (smooth) 5-gon spaces and of 6-gon spaces, under some condition on r ∈ R 6 +. The same formula constitutes a lower bound for all (smooth) spaces of 6-gons. Moreover, we prove that the Gromov width of M(r) is given by the above expression when M(r) is symplectomorphic to CP n−3 , for any n ≥ 4.

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“…Calabi in [5] uses the diastasis to give necessary and sufficient conditions for the existence of an holomorphic isometric immersion of a real analytic Kähler manifolds into a complex space form. For others interesting applications of the diastasis function see [10,11,12,13,14,15,18] and reference therein.…”

Section: Diastasis and Diastasic Entropymentioning

confidence: 99%

Diastatic entropy and rigidity of complex hyperbolic manifolds

Mossa

2016

Complex Manifolds

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Let f : (Y, g) → (X, g 0 ) be a non zero 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].techniques developed in its proof has provided a solution of long-standing problems. Denoted by Ent v (M, g) the volume entropy of a compact Riemannian manifold (M, g) we have:Theorem A (G. Besson, G. Courtois, S. Gallot). Let (Y, g) be a compact Riemannian manifold of dimension n ≥ 3 and let (X, g 0 ) be a compact negatively curved locally symmetric Riemannian manifold of the same dimension of Y . If

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Some remarks on the Gromov width of homogeneous Hodge manifolds

Abstract: ].

Cited by 5 publications

References 13 publications

Minimal symplectic atlases of Hermitian symmetric spaces

Minimal symplectic atlases of Hermitian symmetric spaces

On the Gromov width of homogeneous Kähler manifolds

Diastatic entropy and rigidity of complex hyperbolic manifolds

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