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A variational solution of the A. D. Aleksandrov problem of existence of a convex polytope with prescribed Gauss curvature

Vladimir Oliker (2005)

Banach Center Publications

In his book on convex polytopes [2] A. D. Aleksandrov raised a general question of finding variational formulations and solutions to geometric problems of existence of convex polytopes in ℝ n + 1 , n ≥ 2, with prescribed geometric data. Examples of such problems for closed convex polytopes for which variational solutions are known are the celebrated Minkowski problem [2] and the Gauss curvature problem [20]. In this paper we give a simple variational proof of existence for the A. D. Aleksandrov problem...

A Weitzenbôck formula for the second fundamental form of a Riemannian foliation

Paolo Piccinni (1984)

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

Si considera la seconda forma fondamentale α di foliazioni su varietà riemanniane e si ottiene una formula per il laplaciano ∇ 2 ⁡ α - Se ne deducono alcune implicazioni per foliazioni su varietà a curvatura costante.

Abelian analytic torsion and symplectic volume

B.D.K. McLellan (2015)

Archivum Mathematicum

This article studies the abelian analytic torsion on a closed, oriented, Sasakian three-manifold and identifies this quantity as a specific multiple of the natural unit symplectic volume form on the moduli space of flat abelian connections. This identification computes the analytic torsion explicitly in terms of Seifert data.

Abelian complex structures on 6-dimensional compact nilmanifolds

Luis A. Cordero, Marisa Fernández, Luis Ugarte (2002)

Commentationes Mathematicae Universitatis Carolinae

We classify the 6 -dimensional compact nilmanifolds that admit abelian complex structures, and for any such complex structure J we describe the space of symplectic forms which are compatible with J .

Abelian simply transitive affine groups of symplectic type

Oliver Baues, Vicente Cortés (2002)

Annales de l’institut Fourier

The set of all Abelian simply transitive subgroups of the affine group naturally corresponds to the set of real solutions of a system of algebraic equations. We classify all simply transitive subgroups of the symplectic affine group by constructing a model space for the corresponding variety of solutions. Similarly, we classify the complete global model spaces for flat special Kähler manifolds with a constant cubic form.

Abnormality of trajectory in sub-Riemannian structure

F. Pelletier, L. Bouche (1995)

Banach Center Publications

In the sub-Riemannian framework, we give geometric necessary and sufficient conditions for the existence of abnormal extremals of the Maximum Principle. We give relations between abnormality, C 1 -rigidity and length minimizing. In particular, in the case of three dimensional manifolds we show that, if there exist abnormal extremals, generically, they are locally length minimizing and in the case of four dimensional manifolds we exhibit abnormal extremals which are not C 1 -rigid and which can be minimizing...

About the Calabi problem: a finite-dimensional approach

H.-D. Cao, J. Keller (2013)

Journal of the European Mathematical Society

Let us consider a projective manifold M n and a smooth volume form Ω on M . We define the gradient flow associated to the problem of Ω -balanced metrics in the quantum formalism, the Ω -balancing flow. At the limit of the quantization, we prove that (see Theorem 1) the Ω -balancing flow converges towards a natural flow in Kähler geometry, the Ω -Kähler flow. We also prove the long time existence of the Ω -Kähler flow and its convergence towards Yau’s solution to the Calabi conjecture of prescribing the...

Currently displaying 341 – 360 of 5550