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On compact homogeneous symplectic manifolds

P. B. Zwart, William M. Boothby (1980)

Annales de l'institut Fourier

In this paper the authors study compact homogeneous spaces G / K (of a Lie group G ) on which there if defined a G -invariant symplectic form Ω . It is an important feature of the paper that very little is assumed concerning G and K . The essential assumptions are: (1) G is connected and (2) K is uniform (i.e., G / K is compact). Further, for convenience only and with no loss of generality, it is supposed that G is simply connected and K contains no connected normal subgroup of G , i.e., that G acts almost effectively...

On compact Kähler surfaces

Nicholas Buchdahl (1999)

Annales de l'institut Fourier

Without relying on the classification of compact complex surfaces, it is proved that every such surface with even first Betti number admits a Kähler metric and that a real form of the classical Nakai-Moishezon criterion holds on the surface.

On compact symplectic and Kählerian solvmanifolds which are not completely solvable

Aleksy Tralle (1997)

Colloquium Mathematicae

We are interested in the problem of describing compact solvmanifolds admitting symplectic and Kählerian structures. This was first considered in [3, 4] and [7]. These papers used the Hattori theorem concerning the cohomology of solvmanifolds hence the results obtained covered only the completely solvable case}. Our results do not use the assumption of complete solvability. We apply our methods to construct a new example of a compact symplectic non-Kählerian solvmanifold.

On compatible linear connections of two-dimensional generalized Berwald manifolds: a classical approach

Csaba Vincze, Tahere Reza Khoshdani, Sareh Mehdi Zadeh Gilani, Márk Oláh (2019)

Communications in Mathematics

In the paper we characterize the two-dimensional generalized Berwald manifolds in terms of the classical setting of Finsler surfaces (Berwald frame, main scalar etc.). As an application we prove that if a Landsberg surface is a generalized Berwald manifold then it must be a Berwald manifold. Especially, we reproduce Wagner's original result in honor of the 75th anniversary of publishing his pioneering work about generalized Berwald manifolds.

On complete linear Weingarten hypersurfaces in locally symmetric Riemannian manifolds

Cícero P. Aquino, Henrique F. de Lima, Fábio R. dos Santos, Marco Antonio L. Velásquez (2015)

Commentationes Mathematicae Universitatis Carolinae

Our aim is to apply suitable generalized maximum principles in order to obtain characterization results concerning complete linear Weingarten hypersurfaces immersed in a locally symmetric Riemannian manifold, whose sectional curvature is supposed to obey standard constraints. In this setting, we establish sufficient conditions to guarantee that such a hypersurface must be either totally umbilical or an isoparametric hypersurface with two distinct principal curvatures one of which is simple.

On complexity and motion planning for co-rank one sub-riemannian metrics

Cutberto Romero-Meléndez, Jean Paul Gauthier, Felipe Monroy-Pérez (2004)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we study the motion planning problem for generic sub-riemannian metrics of co-rank one. We give explicit expressions for the metric complexity (in the sense of Jean [10, 11]), in terms of the elementary invariants of the problem. We construct asymptotic optimal syntheses. It turns out that among the results we show, the most complicated case is the 3-dimensional. Besides the generic C ∞ case, we study some non-generic generalizations in the analytic case.

On complexity and motion planning for co-rank one sub-Riemannian metrics

Cutberto Romero-Meléndez, Jean Paul Gauthier, Felipe Monroy-Pérez (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we study the motion planning problem for generic sub-Riemannian metrics of co-rank one. We give explicit expressions for the metric complexity (in the sense of Jean [CITE]), in terms of the elementary invariants of the problem. We construct asymptotic optimal syntheses. It turns out that among the results we show, the most complicated case is the 3-dimensional. Besides the generic C∞ case, we study some non-generic generalizations in the analytic case.

On Conditions for Unrectifiability of a Metric Space

Piotr Hajłasz, Soheil Malekzadeh (2015)

Analysis and Geometry in Metric Spaces

We find necessary and sufficient conditions for a Lipschitz map f : E ⊂ ℝk → X into a metric space to satisfy ℋk(f(E)) = 0. An interesting feature of our approach is that despite the fact that we are dealing with arbitrary metric spaces, we employ a variant of the classical implicit function theorem. Applications include pure unrectifiability of the Heisenberg groups.

Currently displaying 121 – 140 of 791