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Displaying similar documents to “The systolic constant of orientable Bieberbach 3-manifolds”

Holonomy groups of complete flat manifolds

Michał Sadowski (2007)

Banach Center Publications

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We present short direct proofs of two known properties of complete flat manifolds. They say that the diffeomorphism classes of m-dimensional complete flat manifolds form a finite set S C F ( m ) and that each element of S C F ( m ) is represented by a manifold with finite holonomy group.

Estimates of the Kobayashi-Royden metric in almost complex manifolds

Hervé Gaussier, Alexandre Sukhov (2005)

Bulletin de la Société Mathématique de France

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We establish a lower estimate for the Kobayashi-Royden infinitesimal pseudometric on an almost complex manifold ( M , J ) admitting a bounded strictly plurisubharmonic function. We apply this result to study the boundary behaviour of the metric on a strictly pseudoconvex domain in M and to give a sufficient condition for the complete hyperbolicity of a domain in ( M , J ) .

Collapse of warped submersions

Szymon M. Walczak (2006)

Annales Polonici Mathematici

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We generalize the concept of warped manifold to Riemannian submersions π: M → B between two compact Riemannian manifolds ( M , g M ) and ( B , g B ) in the following way. If f: B → (0,∞) is a smooth function on B which is extended to a function f̂ = f ∘ π constant along the fibres of π then we define a new metric g f on M by g f | × g M | × , g f | × T M ̂ f ̂ ² g M | × T M ̂ , where and denote the bundles of horizontal and vertical vectors. The manifold ( M , g f ) obtained that way is called a warped submersion. The function f is called a warping function. We show...

On G -sets and isospectrality

Ori Parzanchevski (2013)

Annales de l’institut Fourier

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We study finite G -sets and their tensor product with Riemannian manifolds, and obtain results on isospectral quotients and covers. In particular, we show the following: If M is a compact connected Riemannian manifold (or orbifold) whose fundamental group has a finite non-cyclic quotient, then M has isospectral non-isometric covers.

Holonomy groups of flat manifolds with the R property

Rafał Lutowski, Andrzej Szczepański (2013)

Fundamenta Mathematicae

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Let M be a flat manifold. We say that M has the R property if the Reidemeister number R(f) is infinite for every homeomorphism f: M → M. We investigate relations between the holonomy representation ρ of M and the R property. When the holonomy group of M is solvable we show that if ρ has a unique ℝ-irreducible subrepresentation of odd degree then M has the R property. This result is related to Conjecture 4.8 in [K. Dekimpe et al., Topol. Methods Nonlinear Anal. 34 (2009)].

On 2 p -dimensional Riemannian manifolds with positive scalar curvature

Domenico Perrone (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In questo lavoro si danno alcuni risultati sugli spettri degli operatori di Laplace per varietà Riemanniane compatte con curvatura scalare positiva e di dimensione 2 p . Ad essi si aggiunge una osservazione riguardante la congettura di Yamabe.

Geometry of manifolds which admit conservation laws

David E. Blair, Alexander P. Stone (1971)

Annales de l'institut Fourier

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Let M be an ( n + 1 ) -dimensional Riemannian manifold admitting a covariant constant endomorphism h of the localized module of 1-forms with distinct non-zero eigenvalues. After it is shown that M is locally flat, a manifold N immersed in M is studied. The manifold N has an induced structure with n of the same eigenvalues if and only if the normal to N is a fixed direction of h . Finally conditions under which N is invariant under h , N is totally geodesic and the induced structure has vanishing...

Riemannian semisymmetric almost Kenmotsu manifolds and nullity distributions

Yaning Wang, Ximin Liu (2014)

Annales Polonici Mathematici

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We consider an almost Kenmotsu manifold M 2 n + 1 with the characteristic vector field ξ belonging to the (k,μ)’-nullity distribution and h’ ≠ 0 and we prove that M 2 n + 1 is locally isometric to the Riemannian product of an (n+1)-dimensional manifold of constant sectional curvature -4 and a flat n-dimensional manifold, provided that M 2 n + 1 is ξ-Riemannian-semisymmetric. Moreover, if M 2 n + 1 is a ξ-Riemannian-semisymmetric almost Kenmotsu manifold such that ξ belongs to the (k,μ)-nullity distribution, we prove...

The ℤ₂-cohomology cup-length of real flag manifolds

Július Korbaš, Juraj Lörinc (2003)

Fundamenta Mathematicae

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Using fiberings, we determine the cup-length and the Lyusternik-Shnirel’man category for some infinite families of real flag manifolds O ( n + . . . + n q ) / O ( n ) × . . . × O ( n q ) , q ≥ 3. We also give, or describe ways to obtain, interesting estimates for the cup-length of any O ( n + . . . + n q ) / O ( n ) × . . . × O ( n q ) , q ≥ 3. To present another approach (combining well with the “method of fiberings”), we generalize to the real flag manifolds Stong’s approach used for calculations in the ℤ₂-cohomology algebra of the Grassmann manifolds.

How to define "convex functions" on differentiable manifolds

Stefan Rolewicz (2009)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In the paper a class of families (M) of functions defined on differentiable manifolds M with the following properties: 1 . if M is a linear manifold, then (M) contains convex functions, 2 . (·) is invariant under diffeomorphisms, 3 . each f ∈ (M) is differentiable on a dense G δ -set, is investigated.

The discriminant and oscillation lengths for contact and Legendrian isotopies

Vincent Colin, Sheila Sandon (2015)

Journal of the European Mathematical Society

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We define an integer-valued non-degenerate bi-invariant metric (the discriminant metric) on the universal cover of the identity component of the contactomorphism group of any contact manifold. This metric has a very simple geometric definition, based on the notion of discriminant points of contactomorphisms. Using generating functions we prove that the discriminant metric is unbounded for the standard contact structures on 2 n × S 1 and P 2 n + 1 . On the other hand we also show by elementary arguments...