CONTENTS -- Preface -- Organizing Committees -- A brief portrait of the life and work of Professor Enrique Vidal Abascal L. A. Cordero -- Part A Foliation theory -- Characteristic classes for Riemannian foliations S. Hurder -- 1. Introduction -- 2. Classifying spaces -- 3. Primary classes -- 4. Secondary classes -- 5. Variation of secondary classes -- 6. Molino Structure Theory -- 7. Some open problems -- References -- Non unique-ergodicity of harmonic measures: Smoothing Samuel Petite's examples B. Deroin -- 1. Introduction -- 2. The construction -- 3. Questions -- Acknowledgement -- References -- On the uniform simplicity of diffeomorphism groups T. Tsuboi -- 1. Introduction -- 2. Uniform perfectness of diffeomorphism groups -- 3. Uniform simplicity of the diffeomorphism groups -- Acknowledgement -- References -- On Bennequin's isotopy lemma and Thurston's inequality Y. Mitsumatsu -- 1. Thurston's Inequality -- 2. Thurston's Absolute Inequality for Spinnable Foliations -- 3. Dehn Filling -- 4. Bennequin's Isotopy Lemma -- Acknowledgements -- References -- On the Julia sets of complex codimension-one transversally holomorphic foliations T. Asuke -- 1. Introduction -- 2. Definition of the Fatou and Julia sets -- 3. Some properties of Julia sets -- 4. Examples -- References -- Singular Riemannian foliations on spaces without conjugate points A. Lytchak -- 1. Introduction -- 2. Preliminaries -- 3. Geometric arguments -- 4. Topological arguments -- Acknowledgments -- References -- Variational formulae for the total mean curvatures of a codimension-one distribution V. Rovenski and P. Walczak -- 0. Introduction -- 1. Main Results -- 2. Proofs -- 2.1. Algebraic preliminaries -- 2.2. Proof of Theorem 0.2 -- 2.3. Variational formulae -- References -- On a Weitzenböck-like formula for Riemannian foliations V. Slesar -- 1. Introduction.

2. Canonical differential operators defined on a Riemannian foliation -- 3. Adiabatic limits and Riemannian foliations -- 4. A transversal Weitzenböck formula -- Acknowledgments -- References -- Duality and minimality for Riemannian foliations on open manifolds X. M. Masa -- 1. The duality -- 2. The minimality -- 3. Singular Riemannian foliations -- References -- Open problems on foliations -- Part B Riemannian geometry -- Graphs with prescribed mean curvature M. Dajczer -- 1. Introduction -- 2. Killing graphs -- 3. Riemannian submersions -- 4. Conformal Killing graphs -- References -- Genuine isometric and conformal deformations of submanifolds R. Tojeiro -- 1. Introduction -- 2. The hypersurface case -- 2.1. Local theory for the isometric case -- 2.2. Global theory of isometrically deformable hypersurfaces -- 2.3. Digression: Extending intrinsic isometries -- 2.4. Local theory of conformal deformations of hypersurfaces -- 3. Higher codimensions: Rigidity results -- 3.1. The s-nullity and the conformal s-nullity -- 3.2. A main tool: flat bilinear forms -- 3.3. Conformal geometry in the light cone -- 4. The general deformation problem -- 5. Genuine deformations -- 5.1. Ruled extensions -- 5.2. Genuine conformal deformations of submanifolds -- 5.3. Constructing conformal pairs from isometric ones -- Acknowledgment -- References -- Totally geodesic submanifolds in Riemannian symmetric spaces S. Klein -- 1. Totally geodesic submanifolds -- 2. Maximal totally geodesic submanifolds in the Riemannian symmetric spaces of rank 2 -- 2.1. G +2 (Rn+2) -- 2.2. G2 (Cn+2) -- 2.3. G (Hn+2) -- 2.4. SU(3)=SO(3) -- 2.5. SU(6)=Sp(3) -- 2.6. SO(10)=U(5) -- 2.7. E6=(U(1) Spin(10)) -- 2.8. E6=F4 -- 2.9. G2=SO(4) -- 2.10. SU(3) -- 2.11. Sp(2) -- 2.12. G2 -- Acknowledgments -- References.

The orbits of cohomogeneity one actions on complex hyperbolic spaces J. C. Díaz-Ramos -- 1. The geometry of the orbits -- 2. Hypersurfaces with constant principal curvatures -- Acknowledgements -- References -- Rigidity results for geodesic spheres in space forms J. Roth -- 1. Introduction -- 2. Preliminaries -- 3. Proof of Theorem 1.1 -- 4. Rigidity results in the Euclidean space -- Acknowledgements -- References -- Mean curvature flow and Bernstein-Calabi results for spacelike graphs G. Li and I. M. C. Salavessa -- 1. Introduction -- 2. Bernstein-Calabi and Heinz-Chern type results -- 3. The mean curvature flow -- 4. Homotopy to a constant map -- Acknowledgements -- References -- Riemannian geometric realizations for Ricci tensors of generalized algebraic curvature operators P. Gilkey, S. Nikcevic and D. Westerman -- 1. Introduction -- 1.1. Realizing Riemannian algebraic curvature tensors -- 1.2. Osserman geometry -- 1.3. Affine geometry -- 1.4. Torsion free connections and Riemannian geometry -- 2. The proof of Theorem 1.3 -- Acknowledgments -- References -- Conformally Osserman multiply warped product structures in the Riemannian setting M. Brozos-Vázquez, M. E. Vázquez-Abal and R. Vázquez-Lorenzo -- 1. Introduction -- 2. Preliminaries -- 3. Conformally Osserman multiply warped products -- 4. Locally conformally at multiply warped products -- 5. Osserman multiply warped products -- 6. Multiply warped products of constant curvature -- Acknowledgements -- References -- Riemannian -symmetric spaces M. Goze and E. Remm -- 1. Riemannian reductive homogeneous spaces -- 2. Riemannian -symmetric spaces -- 2.1. -symmetric spaces -- 2.2. -grading of the Lie algebra g of G -- 2.3. Riemannian and Indefinite Riemannian -symmetric spaces -- 2.4. Irreducible Riemannian -symmetric spaces -- 3. Classification of compact simple Z2 symmetric spaces.

4. On the classification of Riemannian compact Z2 -symmetric spaces -- 4.1. Z2 -symmetric metrics on flag manifolds -- 4.2. The Z2 -Riemannian symmetric space SO(2m)=Sp(m) -- References -- Methods for solving the Jacobi equation. Constant osculating rank vs. constant Jacobi osculating rank T. Arias-Marco -- 1. Introduction and preliminaries -- 2. Preliminaries about H-type groups -- 3. Kaplan's example -- 3.1. Constant osculating rank of the Jacobi operator along a special family of geodesics -- 3.2. Resolution of the Jacobi equation -- 3.3. Relation between both methods -- Acknowledgements -- References -- On the reparametrization of affine homogeneous geodesics Z. Dusek -- 1. Introduction -- 2. Homogeneous geodesics in pseudo-Riemannian manifolds -- 3. Homogeneous geodesics in affine manifolds -- 4. Locally homogeneous connections in dimension two -- 5. G.o. manifolds of type A -- 6. G.o. manifolds of type B -- 7. General connection of type B -- Acknowledgments -- References -- Conjugate connections and differential equations on infinite dimensional manifolds M. Aghasi, C. T. J. Dodson, G. N. Galanis and A. Suri -- 1. Introduction -- 2. Preliminaries -- 3. Classification for vector bundle structures of T2M -- 4. Connections and ordinary differential equations -- 5. The Earle and Eells foliation theorem in Fréchet spaces -- References -- Totally biharmonic submanifolds D. Impera and S. Montaldo -- 1. Introduction -- 2. Biharmonic maps -- 3. Totally biharmonic hypersurfaces -- 4. Totally biharmonic surfaces of space forms -- 5. Biharmonic curves in H3 -- Acknowledgements -- References -- The biharmonicity of unit vector fields on the Poincaré halfspace Hn M. K. Markellos -- 1. Introduction -- 2. Preliminaries -- 2.1. Biharmonic maps -- 2.2. The tangent bundle and the unit sphere bundle -- 3. Homogeneous structures -- Acknowledgements -- References.

Perspectives on biharmonic maps and submanifolds A. Balmus -- 1. Introduction -- 2. Bihamonic maps and warped product manifolds -- 3. Biharmonic submanifolds in space forms -- 4. On the biharmonicity of the Gauss map -- Acknowledgements -- References -- Contact pair structures and associated metrics G. Bande and A. Hadjar -- 1. Introduction -- 2. Preliminaries on contact pairs -- 3. Contact pair structures and almost contact structures -- 3.1. Almost contact structures -- 3.2. Contact pair structures -- 4. Compatible and associated metrics -- 4.1. Orthogonal foliations -- Final comments -- Acknowledgements -- References -- Paraquaternionic manifolds and mixed 3-structures S. Ianus and G. E. Vilcu -- 1. Introduction -- 2. Paraquaternionic structures on manifolds -- 3. Manifolds endowed with mixed 3-structures -- 4. Normal semi-invariant submanifolds and mixed 3-structures -- Acknowledgements -- References -- On topological obstruction of compact positively Ricci curved manifolds W.-H. Chen -- 1. Introduction -- 2. An Extension of Myers' Theorem -- Acknowledgements -- References -- Gray curvature conditions and the Tanaka-Webster connection R. Mocanu -- 1. Different types of Gray curvature conditions -- 2. Gray curvature conditions for the Tanaka-Webster connection -- References -- Riemannian structures on higher order frame bundles from classical linear connections J. Kurek and W. M. Mikulski -- 1. Introduction -- 2. Natural operators -- 3. The main result -- References -- Distributions on the cotangent bundle from torsion-free connections J. Kurek and W. M. Mikulski -- 1. Introduction -- 2. The main result -- 3. Proof of the main result -- References -- On the geodesics of the rotational surfaces in the Bianchi-Cartan-Vranceanu spaces P. Piu and M. M. Profir -- 1. Introduction -- 2. Geodesics on surfaces of revolution -- 3. The Clairaut's relation.

4. Geodesics on the cylinder.