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Elementary Differential Geometry

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Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers

Part of the book series: Mathematical Engineering ((MATHENGIN,volume 21))

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Abstract

We consider an N-dimensional Riemannian manifold M, and let g i be a basis at the point P i (u 1, …, u N) and g j be another basis at the other point P j (u 1, …,u N). Note that each such basis may only exist in a local neighborhood of the respective points and not necessarily for the whole space. For each such point, we may construct an embedded affine tangential manifold.

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References

  • Bär C (2001) Elementare differential geometrie. Zweite, De Gruyter, Berlin/New York (in German)

    Google Scholar 

  • Chase HS (2012) Fundamental forms of surfaces and the Gauss-Bonnet theorem. University of Chicago, Chicago

    Google Scholar 

  • Danielson DA (2003) Vectors and tensors in engineering and physics, 2nd edn. ABP, Westview Press, Colorado

    Google Scholar 

  • Fecko M (2011) Differential geometry and lie groups for physicists. Cambridge University Press, Cambridge

    Google Scholar 

  • Grinfeld P (2013) Introduction to tensor analysis and the calculus of moving surfaces. Springer Science+Business Media, New York

    Google Scholar 

  • Klingbeil E (1966) Tensorrechnung für ingenieure. B.I.-Wissenschafts-verlag, Mannheim/Wien/Zürich

    Google Scholar 

  • Kühnel W (2013) Differentialgeometrie—Kurven, Flächen, Mannigfaltigkeit, 6th edn. Springer-Spektrum, Wiesbaden (in German)

    Google Scholar 

  • Lang S (2001) Fundamentals of differential geometry, 2nd edn. Springer, New York/Berlin

    Google Scholar 

  • Penrose R (2005) The road to reality. Alfred A. Knopf, New York

    Google Scholar 

  • Schutz B (1980) Geometrical methods of mathematical physics. Cambridge University Press (CUP), Cambridge

    Google Scholar 

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Authors and Affiliations

  1. EM-motive GmbH (A Joint Company of Daimler and Bosch), 71636, Ludwigsburg, Germany

    Hung Nguyen-Schäfer

  2. Interdisciplinary Center for Scientific Computing (IWR), University of Heidelberg, 69120, Heidelberg, Germany

    Jan-Philip Schmidt

Authors
  1. Hung Nguyen-Schäfer
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  2. Jan-Philip Schmidt
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Correspondence to Hung Nguyen-Schäfer .

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© 2014 Springer-Verlag Berlin Heidelberg

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Nguyen-Schäfer, H., Schmidt, JP. (2014). Elementary Differential Geometry. In: Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers. Mathematical Engineering, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43444-4_3

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  • DOI: https://doi.org/10.1007/978-3-662-43444-4_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-43443-7

  • Online ISBN: 978-3-662-43444-4

  • eBook Packages: EngineeringEngineering (R0)

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