A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature. Experts in the fields of Riemannian, Lorentzian and contact geometry present  state-of-the-art reviews of their topics. The contributions are written on a graduate level and contain  extended bibliographies. The ten chapters are the result of various doctoral courses which were held in 2009 and 2010 at universities in Leuven, Serbia, Romania and Spain.

A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature. Experts in the fields of Riemannian, Lorentzian and contact geometry present  state-of-the-art reviews of their topics. The contributions are written on a graduate level and contain  extended bibliographies. The ten chapters are the result of various doctoral courses which were held in 2009 and 2010 at universities in Leuven, Serbia, Romania and Spain.

This workshop collected together works by experts working in various aspects of the differential geometry of submanifold and discussed recent advances and unsolved problems. Two important linking lectures were on the work done by Thorbergsson and others on classifying isoparametric submanifolds of Euclidean spaces and the generalisation of these to Hilbert spaces due to Terng and others. Isoparametric submanifolds provides examples of minimal, taut submanifolds, of harmonic maps and submanifolds with parallel second fundamental form-all topics discussed at this workshop. There were also lectures on the rapidly developing topic of the affine geometry of hypersurfaces and on applications. Amomg the applications discussed are new methods for using PDE's for generating surfaces with special shapes for use in engineering design.

This proceedings on pure and applied differential geometry, discusses several subjects in submanifold theory, such as the Willmore problem, minimal surfaces, submanifolds of finite type, affine differential geometry, indefinite Riemannian geometry, and applications of differential geometry in human and artificial vision.

The topics covered are pure differential geometry, especially submanifolds and affine differential geometry, and applications of geometry to human vision, robotics, and gastro-entrology.

A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature. Experts in the fields of Riemannian, Lorentzian and contact geometry present  state-of-the-art reviews of their topics. The contributions are written on a graduate level and contain  extended bibliographies. The ten chapters are the result of various doctoral courses which were held in 2009 and 2010 at universities in Leuven, Serbia, Romania and Spain.

A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature. Experts in the fields of Riemannian, Lorentzian and contact geometry present  state-of-the-art reviews of their topics. The contributions are written on a graduate level and contain  extended bibliographies. The ten chapters are the result of various doctoral courses which were held in 2009 and 2010 at universities in Leuven, Serbia, Romania and Spain.

This workshop collected together works by experts working in various aspects of the differential geometry of submanifold and discussed recent advances and unsolved problems. Two important linking lectures were on the work done by Thorbergsson and others on classifying isoparametric submanifolds of Euclidean spaces and the generalisation of these to Hilbert spaces due to Terng and others. Isoparametric submanifolds provides examples of minimal, taut submanifolds, of harmonic maps and submanifolds with parallel second fundamental form-all topics discussed at this workshop. There were also lectures on the rapidly developing topic of the affine geometry of hypersurfaces and on applications. Amomg the applications discussed are new methods for using PDE's for generating surfaces with special shapes for use in engineering design.

This proceedings on pure and applied differential geometry, discusses several subjects in submanifold theory, such as the Willmore problem, minimal surfaces, submanifolds of finite type, affine differential geometry, indefinite Riemannian geometry, and applications of differential geometry in human and artificial vision.

The topics covered are pure differential geometry, especially submanifolds and affine differential geometry, and applications of geometry to human vision, robotics, and gastro-entrology.