Fernando Etayo

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By using several tools coming from Real Algebraic Geometry, Computer Algebra and Projective Geometry (Sturm–Habicht sequences and the classification of pencils of conics in P 2 (R)), a new approach for characterizing the ten relative positions of two ellipses is introduced. Each relative position is exclusively characterized by a set of equalities and(More)
We show that which that for a Berwald structure, any Rie-mannian structure that is preserved by the Berwald connection leaves the indicatrix invariant under horizontal parallel transport. We also obtain the converse result: if (M, F) is a Finsler structure such that there exists a Rie-mannian structure that leaves invariant the indicatrix under parallel(More)
Manifolds endowed with three foliations pairwise transversal are known as 3-webs. Equivalently, they can be algebraically defined as biparacom-plex or complex product manifolds, i.e., manifolds endowed with three tensor fields of type (1, 1), F , P and J = F • P , where the two first are product and the third one is complex, and they mutually anti-commute.(More)
This is a survey on bi-Lagrangian manifolds, which are symplectic manifolds endowed with two transversal Lagrangian foliations. We also study the non-integrable case (i.e., a symplectic manifold endowed with two transversal Lagrangian distributions). We show that many different geometric structures can be attached to these manifolds and we carefully analyse(More)
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