2 citations · 3 across the 8 of their papers we have counts for
8 papers
Contact detection between an ellipsoid and a combination of quadrics
Miguel Brozos-Vázquez, M. J. Pereira-Sáez, A. B. Rodríguez-Raposo +2
We analyze the characteristic polynomial associated to an ellipsoid and another quadric in the context of the contact detection problem. We obtain a necessary and sufficient condit…
Homotopic distance and generalized motion planning
E. Macías-Virgós, D. Mosquera-Lois, M. J. Pereira-Sáez
We prove that the homotopic distance between two maps defined on a manifold is bounded above by the sum of their subspace distances on the critical submanifol of any Morse-Bott fun…
Relative singular value decomposition and applications to LS-category
E. Macías-Virgós, M. J. Pereira-Sáez, Daniel Tanré
Let be the symplectic group of quaternionic -matrices. For any , an element of can be decomposed in $A= \begin{bmatrix} α&T\cr β&P \…
Classification of the relative positions between an ellipsoid and an elliptic paraboloid
Miguel Brozos-Vázquez, María José Pereira-Sáez, María José Souto-Salorio +1
We classify all the relative positions between an ellipsoid and an elliptic paraboloid when the ellipsoid is small in comparison with the paraboloid ({\it small} meaning that the e…
Height functions on compact symmetric spaces
E. Macías-Virgós, M. J. Pereira-Sáez
We consider height functions on symmetric spaces embedded in the associated matrix Lie group . In particular we study the relationship between the critical sets of…
A topological approach to left eigenvalues of quaternionic matrices
E. Macías-Virgós, M. J. Pereira-Sáez
It is known that a quaternionic matrix has one, two or an infinite number of left eigenvalues, but the available algebraic proofs are difficult to generalize to higher…
An upper bound for the Lusternik-Schnirelmann category of the symplectic group
E. Macías-Virgós, M. J. Pereira-Sáez
We prove that the LS category of the symplectic group is bounded above by . This is achieved by computing the number of critical levels of a height function…
Trace map, Cayley transform and LS category of Lie groups
A. Gómez-Tato, E. Macías-Virgós, M. J. Pereira-Sáez
The aim of this paper is to use the so-called Cayley transform to compute the LS category of Lie groups and homogeneous spaces by giving explicit categorical open coverings. When a…