Journal of Geometry

, Volume 69, Issue 1–2, pp 73–78 | Cite as

On the canonical extension of a differentiable manifold

  • Mehmet Yildirim
  • Erdoğan Esin
Article
Received:

Abstract

In this paper, the differential geometry of second canonical extension2M of a differentiable manifoldM is studied. Some vector fields tangent to2M inTTM are determined. In addition we obtain that the second canonical extensions ofM and a totally geodesic submanifold inM are totally geodesic submanifolds inTTM and2M respectively.

Keywords

Vector Field Differential Geometry Differentiable Manifold Canonical Extension Geodesic Submanifolds 
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References

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    R.H. Bowman, On differentiable extensions, Tensor,N.S. 21 (1970), 139–150.Google Scholar
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    K. Yano andS. Ishihara,Tangent and Cotangent Bundle, Mercel Dekker Inc., New York 1973.Google Scholar

Copyright information

© Birkhäuser Verlag 2000

Authors and Affiliations

  • Mehmet Yildirim
    • 1
  • Erdoğan Esin
    • 2
  1. 1.Department of MathematicsKirikkale UniversityKinkkaleTurkey
  2. 2.Department of MathematicsGazi UniversityAnkaraTurkey

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