Topics in modern differential geometry

Description

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. Read more... Abstract: 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 Front Matter....Pages i-vii The Riemannian and Lorentzian Splitting Theorems....Pages 1-20 Periodic Trajectories of Dynamical Systems Having a One-Parameter Group of Symmetries....Pages 21-36 Geometry and Materials....Pages 37-48 On Deciding Whether a Submanifold Is Parabolic or Hyperbolic Using Its Mean Curvature....Pages 49-77 Contact Forms in Geometry and Topology....Pages 79-94 Farkas and János Bolyai....Pages 95-109 Spectrum Estimates and Applications to Geometry....Pages 111-198 Some Variational Problems on Curves and Applications....Pages 199-222 Special Submanifolds in Hermitian Manifolds....Pages 223-258 An Introduction to Certain Topics on Lorentzian Geometry....Pages 259-284