Riemannian Manifolds


In many cases, the manifolds of interest possess a metric tensor which defines an inner product between tangent vectors at each point of the manifold. Some examples are the submanifolds of an Euclidean space and the space–time, in the context of special or general relativity.


Vector Field Riemannian Manifold Scalar Curvature Curvature Tensor Integral Curve 
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  1. Born, M. and Wolf, E. (1999). Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University Press, Cambridge). Google Scholar
  2. Conlon, L. (2001). Differentiable Manifolds, 2nd ed. (Birkhäuser, Boston). Google Scholar
  3. do Carmo, M. (1992). Riemannian Geometry (Birkhäuser, Boston). Google Scholar
  4. Fisher, S.D. (1999). Complex Variables, 2nd ed. (Dover, New York). Google Scholar
  5. Hirsch, M. and Smale, S. (1974). Differential Equations, Dynamical Systems, and Linear Algebra (Academic Press, New York). Google Scholar
  6. Lee, J.M. (1997). Riemannian Manifolds: An Introduction to Curvature (Springer, New York). Google Scholar
  7. O’Neill, B. (2006). Elementary Differential Geometry, 2nd ed. (Academic Press, New York). Google Scholar
  8. Oprea, J. (1997). Differential Geometry and Its Applications (Prentice-Hall, Upper Saddle River). Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Instituto de CienciasUniversidad Autónoma de PueblaPueblaMexico

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