6 citations · 11 across the 19 of their papers we have counts for
20 papers
The topology of tridiagonal isospectral sets
David Martínez Torres
We describe the topology of the set of tridiagonal symmetric real matrices with fixed non-simple spectrum. The tridiagonal isospectral set is not a submanifold of the corresponding…
Diagonalization of the Toda flow for arbitrary isospectral symmetric matrices
David Martínez Torres, Carlos Tomei
We construct coordinates on orthogonal conjugacy classes of traceless real symmetric matrices with arbitrary spectrum (the isospectral manifold) that diagonalize the non-periodic T…
Diagonalization of the Toda flow on conjugacy classes of matrices with simple spectrum
David Martínez Torres, Carlos Tomei
We construct coordinates on conjugacy classes of traceless complex matrices with simple spectrum that diagonalize the non-periodic Toda vector field. By this we mean that the coord…
Poisson Manifolds of Compact Types with an Appendix by Joshua Mundinger
Marius Crainic, Rui Loja Fernandes, David Martínez Torres +1
We develop the theory of Poisson and Dirac manifolds of compact types, a broad generalization in Poisson and Dirac geometry of compact Lie algebras and Lie groups. We establish key…
Linearizing Toda and SVD flows on large phase spaces of matrices with real spectrum
Ricardo S. Leite, Nicolau C. Saldanha, David Martínez Torres +1
We consider different phase spaces for the Toda flows and the less familiar SVD flows. For the Toda flow, we handle symmetric and non-symmetric matrices with real simple eigenvalue…
Non-exactness of toric Poisson structures
David Martínez Torres, Marcelo Silva
We prove that a Poisson structure on a projective toric variety which is invariant by the torus action and whose symplectic leaves are the torus orbits is not exact. This is deduce…
PDEs from matrices with orthogonal columns
David Martínez Torres
We discuss a system of third order PDEs for strictly convex smooth functions on domains of Euclidean space. We argue that it may be understood as a closure of sorts of the first or…
Coregular submanifolds and Poisson submersions
Lilian C. Brambila, Pedro Frejlich, David Martínez Torres
We analyze \emph{submersions with Poisson fibres}. These are submersions whose total space carries a Poisson structure, on which the ambient Poisson structure pulls back, as a Dira…
An atlas adapted to the Toda flow
David Martínez Torres, Carlos Tomei
We introduce an atlas adapted to the Toda flow on the manifold of full flags of any non-compact real semisimple Lie algebra, and on its Hessenberg-type submanifolds. In our local c…
Nontrivial bundles of coadjoint orbits over
David Martínez Torres, Ignasi Mundet i Riera
Let be a compact connected semisimple Lie group with Lie algebra . Let be a coadjoint orbit. The action of on …
Proper Lie groupoids are real analytic
David Martínez Torres
We show that any proper Lie groupoid admits a compatible (real) analytic structure.
Weakly Hamiltonian actions
David Martínez Torres, Eva Miranda
In this paper we generalize constructions of non-commutative integrable systems to the context of weakly Hamiltonian actions on Poisson manifolds. In particular we prove that abeli…
The diffeomorphism type of canonical integrations of Poisson tensors on surfaces
David Martínez Torres
A surface endowed with a Poisson tensor is known to admit a canonical integration , which is a 4-dimensional manifold with a (symplectic) groupoid structure…
Semisimple coadjoint orbits and cotangent bundles
David Martínez Torres
Semisimple (co)adjoint orbits through real hyperbolic elements are well-known to be symplectomorphic to cotangent bundles. We provide a new proof of this fact based on elementary r…
A note on symplectic topology of -manifolds
Pedro Frejlich, David Martínez Torres, Eva Miranda
A Poisson manifold $(M^{2n},\p)$ is -symplectic if $\bigwedge^n\p$ is transverse to the zero section. In this paper we apply techniques native to Symplectic Topology to address…
A Poisson manifold of strong compact type
David Martínez Torres
We construct a corank one Poisson manifold which is of strong compact type, i.e., the associated Lie algebroid structure on its cotangent bundle is integrable, annd the source 1-co…
Generic linear systems for projective CR manifolds
David Martinez Torres
For compact CR manifolds of hypersurface type which embed in complex projective space, we show that for all k large enough there exist linear systems of which wh…
Codimension one foliations calibrated by non-degenerate closed 2-forms
D. Martinez Torres
A class of codimension one foliations has been recently introduced by imposing a natural compatibility condition with a closed maximally non-degenerate 2-form. In this paper we stu…
The geometry of 2-calibrated manifolds
David Martinez Torres
We define 2-calibrated structures, which are analogs of symplectic structures in odd dimensions. We show the existence of differential topological constructions compatible with the…
Global classification of generic multi-vector fields of top degree
David Martinez Torres
For any compact oriented manifold , we show that that the top degree multi-vector fields transverse to the zero section of are classified, up to orientat…