Results 111 to 120 of about 796 (142)
Purely coclosed G2‐structures on nilmanifolds
Mathematische Nachrichten, 2023 Abstract We classify seven‐dimensional nilpotent Lie groups, decomposable or of nilpotency step at most 4, endowed with left‐invariant purely coclosed G2‐structures. This is done by going through the list of all seven‐dimensional nilpotent Lie algebras given by Gong, providing an example of a left‐invariant 3‐form φ which is a pure coclosed G2 ...
Giovanni Bazzoni +2 more
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AFFINE STRUCTURES ON NILMANIFOLDS
International Journal of Mathematics, 1996We investigate the existence of affine structures on nilmanifolds Γ\G in the case where the Lie algebra g of the Lie group G is filiform nilpotent of dimension less or equal to 11. Here we obtain examples of nilmanifolds without any affine structure in dimensions 10, 11. These are new counterexamples to the Milnor conjecture.
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1992
The author uses the techniques of rational homotopy theory to prove that for a nilmanifold \(M\), we have: \(\dim M=\text{rank}(\pi_ 1(M))=\text{cat}(M)=e_ 0(M)\). Here \(e_ 0(M)\) is the invariant introduced by Toomer and defined as the largest integer \(p\) such that \(E^{p,*}_ \infty\neq 0\) in the Moore spectral sequence: \(\text{Tor}_{H^*(\Omega M;
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The author uses the techniques of rational homotopy theory to prove that for a nilmanifold \(M\), we have: \(\dim M=\text{rank}(\pi_ 1(M))=\text{cat}(M)=e_ 0(M)\). Here \(e_ 0(M)\) is the invariant introduced by Toomer and defined as the largest integer \(p\) such that \(E^{p,*}_ \infty\neq 0\) in the Moore spectral sequence: \(\text{Tor}_{H^*(\Omega M;
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A Decomposition Theorem for Complex Nilmanifolds
Canadian Mathematical Bulletin, 1987AbstractA complex nilmanifold X is isomorphic to a product X ⋍ ℂp x N/┌, where N is a simply connected nilpotent complex Lie group and ┌ is a discrete subgroup of N not contained in a proper connected complex subgroup of N. The pair (N, ┌) is uniquely determined up to holomorphic group isomorphisms.
Loeb, Jean-Jacques +2 more
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THERE ARE ONLY FINITELY MANY INFRA-NILMANIFOLDS UNDER EACH NILMANIFOLD
The Quarterly Journal of Mathematics, 1988Let G be a connected and simply connected nilpotent Lie group and K a maximal compact subgroup of Aut(G). By an (infra-)nilmanifold one means the coset space \(E\setminus G\) where S is a torsion-free discrete uniform lattice of G (G\(\circ K\) resp.). The main result of this work is the following theorem.
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Symplectic structures¶on Heisenberg-type nilmanifolds
manuscripta mathematica, 2000The authors consider certain nilmanifolds of the form \(T \times\Gamma \setminus N\), where \(T\) is a torus and \(\Gamma\) a discrete co-compact subgroup of a 2-step nilpotent Lie group \(N\). The exterior powers of Lie algebra, \(\wedge^* {\mathfrak n}\), are used to study the existence and classification of symplectic and Kähler structures on \(T ...
Dotti, Isabel, Tirao, Paulo
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2013
Nilmanifolds and solvmanifolds appear as “toy-examples” in non-Kahler geometry: indeed, on the one hand, non-tori nilmanifolds admit no Kahler structure, (Benson and Gordon, Topology 27(4):513–518, 1988; Lupton and Oprea, J. Pure Appl. Algebra 91(1–3):193–207, 1994), and, more in general, solvmanifolds admitting a Kahler structure are characterized ...
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Nilmanifolds and solvmanifolds appear as “toy-examples” in non-Kahler geometry: indeed, on the one hand, non-tori nilmanifolds admit no Kahler structure, (Benson and Gordon, Topology 27(4):513–518, 1988; Lupton and Oprea, J. Pure Appl. Algebra 91(1–3):193–207, 1994), and, more in general, solvmanifolds admitting a Kahler structure are characterized ...
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On Algebraic Anosov Diffeomorphisms on Nilmanifolds
Siberian Mathematical Journal, 2004Summary: The article is devoted to the algebraic approaches to Anosov diffeomorphisms. All examples of Anosov diffeomorphisms known so far are connected directly or indirectly with compact nilmanifolds. We consider some new necessary conditions for the existence of these diffeomorphisms on nilmanifolds.
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Periodic Points on Nilmanifolds
1981Shub and Sullivan [13] proves that every C1-map f : M → M of a compact smooth manifold has infinitely many periodic points if the Lefschetz numbers L(fk), k = 1,2,..., are unbounded. This is not generally true if f is a continuous map, and even if f is a homeo-morphism (see [11]).
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Polynomial Eulerian Characteristic of Nilmanifolds
Functional Analysis and Its ApplicationsThe author gives a comprehensive description of the geometry and algebraic topology of the nilmanifold \(M^n = L^n /\Gamma^n\) with \(L^n\) the Lie group of polynomials \(p(t) = t + x_1t^2 + \cdots + x_nt^{n+1}\) with \(x_i \in \mathbb{R}\) and \(\Gamma^n\) the integer lattice with all \(x_i \in \mathbb{Z}.\) Results include the identification of the ...
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