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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)

- Ricardo Gallego Torrome, Fernando Etayo, Spain
- 2009

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)

- Fernando Etayo, Rafael Santamaŕıa
- 2005

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)

- Fernando Etayo, Rafael Santamaŕıa, Sergiu I. Vacaru
- 2008

We outline an unified approach to geometrization of Lagrange mechanics, Finsler geometry and geometric methods of constructing exact solutions with generic off–diagonal terms and nonholonomic variables in gravity theories. Such geometries with induced almost symplectic structure are modelled on nonholonomic manifolds provided with nonintegrable… (More)

- Fernando Etayo, Rafael Santamaŕıa
- 2004

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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