1,721,021 research outputs found
Minimal algebras and 2-step nilpotent Lie algebras in dimension 7
No full textUsiamo i metodi di Bazzoni e Muñoz (Trans Am Math Soc 364:1007–1028, 2012) per ottenere una classificazione delle algebre minimali in dimensione 7, generate in grado 1, su un campo k di caratteristica char(k)≠2 , la cui filtrazione caratteristica ha lunghezza 2. In modo equivalente, classifichiamo algebre di Lie nilpotenti a 2 passi in dimensione 7. Tale classificazione recupera inoltre il tipo di omotopia reale delle 2-nilvarietà in dimensione 7.We use the methods of Bazzoni and Muñoz (Trans Am Math Soc 364:1007–1028, 2012) to give a classification of 7-dimensional minimal algebras, generated in degree 1, over any field k of characteristic char(k)≠2 , whose characteristic filtration has length 2. Equivalently, we classify 2-step nilpotent Lie algebras in dimension 7. This classification also recovers the real homotopy type of 7-dimensional 2-step nilmanifolds
Locally conformally symplectic and Kähler geometry
No full textThe goal of this note is to give an introduction to locally conformally symplectic and Kähler geometry. In particular, Sections 1 and 3 aim to provide the reader with enough mathematical background to appreciate this kind of geometry. The reference book for locally conformally Kähler geometry is "Locally conformal K"ahler Geometry" by Sorin Dragomir and Liviu Ornea. Many progresses in this field, however, were accomplished after the publication of this book, hence are not contained there. On the other hand, there is no book on locally conformally symplectic geometry and many recent advances lie scattered in the literature. Sections 2 and 4 would like to demonstrate how these geometries can be used to give precise mathematical formulations to ideas deeply rooted in classical and modern Physics
Vaisman nilmanifolds
No full textWe prove that if a compact nilmanifold Γ∖G is endowed with a Vaisman structure, then G is isomorphic to the Cartesian product of the Heisenberg group with R
Toric actions and convexity in cosymplectic geometry
No full textWe prove a convexity theorem for Hamiltonian torus actions on compact cosymplectic manifolds. We show that compact toric cosymplectic manifolds are mapping tori of equivariant symplectomorphisms of toric symplectic manifolds
MODULI SPACES OF (CO)CLOSED G2-STRUCTURES ON NILMANIFOLDS
No full textWe compute the dimensions of some moduli spaces of left-invariant closed and coclosed G(2)-structures on 7-dimensional nilmanifolds, showing that they are not related to the third Betti number. We also prove that, in contrast to the case of closed G(2)-structures, the group of automorphisms of a coclosed G(2)-structure is not necessarily abelian
Complex symplectic Lie algebras with large Abelian subalgebras
Full text linkWe present two constructions of complex symplectic structures on Lie algebras with large Abelian ideals. In particular, we completely classify complex symplectic structures on almost Abelian Lie algebras. By considering compact quotients of their corresponding connected, simply connected Lie groups we obtain many examples of complex symplectic manifolds which do not carry (hyper)kahler metrics. We also produce examples of compact complex symplectic manifolds endowed with a fibration whose fibers are Lagrangian tori.(c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons .org /licenses /by -nc -nd /4 .0/)
A 6-dimensional simply connected complex and symplectic manifold with no Kähler metric
No full textWe construct a simply connected compact manifold which has complex and symplectic structures but does not admit K"ahler metrics, in the lowest possible dimension where this can happen, that is, dimension 6. Such a manifold is automatically formal and has even odd-degree Betti numbers but it does not satisfy the Lefschetz property for any symplectic form
A splitting theorem for compact Vaisman manifolds
No full textWe extend to metric compact mapping tori a splitting result for coK"ahler manifolds. In particular, we prove that a compact Vaisman manifold is finitely covered by the product of a Sasakian manifold and a circle
Non-formal co-symplectic manifoldS
No full textStudiamo la formalità del mapping torus di un diffeomorfismo che preserva l'orientazione di una varietà. In particolare, diamo condizioni che garantiscono che un mapping torus abbia un prodotto di Massey non-zero. Come applicazione proviamo che esiste una varietà co-simplettica compatta non formale di dimensione m e con primo numero di Betti b se e solo se m=3 e b > 1, o m>=5 e b>=1. Diamo esempi espliciti di ciascuno di questi casi.We study the formality of the mapping torus of an orientationpreserving diffeomorphism of a manifold. In particular, we give conditions under which a mapping torus has a non-zero Massey product. As an application we prove that there are non-formal compact co-symplectic manifolds of dimension m and with first Betti number b if and only if m = 3 and b ≥ 2, or m ≥ 5 and b ≥ 1. Explicit examples for each one of these cases are given
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