Yet Another Application of the Theory of ODE in the Theory of Vector Fields

Author

Department of Mathematics, Tafresh University, Tafresh, P.C 39518-79611, Iran

Abstract

In this paper we are supposed to define the θ−vector field on the n−surface S and then investigate about the existence and uniqueness of its integral curves by the Theory of Ordinary Differential Equations. Then the
subject is followed through some examples.

Keywords

References

1. M. do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall, Englewood Cliffs, USA, NJ (1977).
2. T. Frankel, The Geometry of Physics, (3rd ed.), Cambridge University Press, New York (2012).
3. W. Hurewicz, Lectures on ordinary Differential Equations, M.I.T Press, Cambridge, Mass (1958).
4. M. Spivak, A Comprehensive Introduction to Differential Geometry, Vol. 1, 3rd Edition, Publish or Perish, Boston (1975).
5. M. Spivak, Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus, W.A Benjamin, Inc., New York (1965).
6. R.H. Wasserman, Tensors and Manifolds with Applications to Mechanics and Relativity, Oxford University Press (1992).
Global Analysis and Discrete Mathematics
Volume 1, Issue 2 - Serial Number 2
November 2016
Pages 65-71

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History

  • Receive Date: 27 July 2015
  • Revise Date: 15 November 2015
  • Accept Date: 30 November 2015

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