1,720,959 research outputs found
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
Sasaki structures distinguished by their basic Hodge numbers
Full text linkIn all odd dimensions we produce examples of manifolds admitting
pairs of Sasaki structures with different basic Hodge numbers. In dimension
we prove more precise results, for example we show that on connected sums of
copies of the number of Sasaki structures with different basic
Hodge numbers within a fixed homotopy class of almost contact structures is
unbounded. All the Sasaki structures we consider are negative in the sense that
the basic first Chern class is represented by a negative definite form of type
. We also discuss the relation of these results to contact topology.Comment: final version, to appear in Bull. London Math. Societ
Sasakian immersions of Sasaki-Ricci solitons into Sasakian space forms
No full textLet (g, X) be a Sasaki-Ricci soliton on a Sasakian manifold S. We prove that if (S, g) admits a local Sasakian immersion in a Sasakian space form S(N, c) of constant phi-sectional curvature c, then S is eta-Einstein and its eta-Einstein constants are a linear function of c with rational coefficients. Moreover, if c <= -3, S is locally equivalent to the Sasakian space form S(n, c). Further results are obtained in the compact setting, i.e. when c > -3, under additional hypotheses
Engel structures on complex surfaces
Full text linkWe classify complex surfaces (M,J) admitting Engel structures D which are complex line bundles. Namely, we prove that this happens if and only if (M,J) has trivial Chern classes. We construct examples of such Engel structures by adapting a construction due to Geiges [7]. We also study associated Engel defining forms and define a unique splitting of TM associated with D J-Engel
Sasaki versus Kähler groups
Full text linkWe study fundamental groups of compact Sasaki manifolds and show that compared to Kähler groups, they exhibit rather different behaviour. This class of groups is not closed under taking direct products, and there is often an upper bound on the dimension of a Sasaki manifold realising a given group. The richest class of Sasaki groups arises in dimension 5
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
Immersions into Sasakian space forms
Full text linkWe study immersions of Sasakian manifolds into finite and infinite dimensional Sasakian space forms. After proving Calabi\u27s rigidity results in the Sasakian setting, we characterise all homogeneous Sasakian manifolds which admit a (local) Sasakian immersion into a nonelliptic Sasakian space form. Moreover, we give a characterisation of homogeneous Sasakian manifolds which can be embedded into the standard sphere both in the compact and noncompact case
Maximally non-integrable almost complex structures: an -principle and cohomological properties
Full text linkWe study almost complex structures with lower bounds on the rank of the
Nijenhuis tensor. Namely, we show that they satisfy an -principle. As a
consequence, all parallelizable manifolds and all manifolds of dimension
(respectively ) admit a almost complex structure whose
Nijenhuis tensor has maximal rank everywhere (resp. is nowhere trivial). For
closed -manifolds, the existence of such structures is characterized in
terms of topological invariants. Moreover, we show that the Dolbeault
cohomology of non-integrable almost complex structures is often infinite
dimensional (even on compact manifolds).Comment: 19 pages, misprint corrected in reference [5], to appear in Selecta
Mathematic
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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