## Topics in Modern Differential GeometryA 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. |

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### Contents

1 | |

Periodic Trajectories of Dynamical Systems Having a OneParameter Group of Symmetries | 21 |

Geometry and Materials | 37 |

On Deciding Whether a Submanifold Is Parabolic or Hyperbolic Using Its Mean Curvature | 49 |

Contact Forms in Geometry and Topology | 79 |

Farkas and János Bolyai | 95 |

Spectrum Estimates and Applications to Geometry | 110 |

Some Variational Problems on Curves and Applications | 199 |

Special Submanifolds in Hermitian Manifolds | 223 |

An Introduction to Certain Topics on Lorentzian Geometry | 259 |

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ball property Bolyai Busemann functions complete minimal complex space form constant sectional curvature contact form contact manifolds contact Riemannian contact structure Corollary defined denote Differential Geometry dimension distance function dynamical system eigenvalue equation essential spectrum exists extrinsic fibers Gauss geodesic ball geodesically complete Geom given global grad Hermitian manifold Hess Hessian holomorphic Hopf hyperbolic hypersurface inequality infinitesimal symmetry invariant isometry János Kaehler manifold Kaehler submanifold Kaehlerian slant Killing vector field Laplacian Lemma Lorentzian manifold Lorentzian metric Math mean curvature mean curvature vector metric g minimal submanifolds minimal surfaces n-dimensional obtain open set orientable orthonormal parabolic plane proof Proposition proved radial radius Remark resp result Ricci curvature Riemannian manifold Riemannian metric Riemannian submersion satisfies sectional curvature semi-Riemannian slant submanifold Splitting Theorem symplectic tangent timelike topology totally real totally real submanifold trajectory Willmore