Topics in Modern Differential Geometry

1. Front Matter

   Pages i-vii

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2. The Riemannian and Lorentzian Splitting Theorems

   • José Luis Flores

   Pages 1-20

3. Periodic Trajectories of Dynamical Systems Having a One-Parameter Group of Symmetries

   • Roberto Giambò, Paolo Piccione

   Pages 21-36

4. Geometry and Materials

   • Bennett Palmer

   Pages 37-48

5. On Deciding Whether a Submanifold Is Parabolic or Hyperbolic Using Its Mean Curvature

   • Vicente Palmer

   Pages 49-77

6. Contact Forms in Geometry and Topology

   • Gheorghe Pitiş

   Pages 79-94

7. Farkas and János Bolyai

   • Mileva Prvanović

   Pages 95-109

8. Spectrum Estimates and Applications to Geometry

   • G. Pacelli Bessa, L. Jorge, L. Mari, J. Fábio Montenegro

   Pages 111-198

9. Some Variational Problems on Curves and Applications

   • Angel Ferrández

   Pages 199-222

10. Special Submanifolds in Hermitian Manifolds

    • Ion Mihai

    Pages 223-258

11. An Introduction to Certain Topics on Lorentzian Geometry

    • Alfonso Romero

    Pages 259-284

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.

• Differential Geometry
• Lorentzian Geometry
• Riemannian Geometry
• Contact Structures
• Anisotropic Surfaces

• Department of Teacher Education, Thomas More University College Department of Teacher Education, Vorselaar, Belgium

  Stefan Haesen

• Department of Mathematics, University of Leuven Department of Mathematics, Leuven, Belgium

  Leopold Verstraelen

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