Tangent Bundle of the Hypersurfaces in a Euclidean Space

  title={Tangent Bundle of the Hypersurfaces in a Euclidean Space},
  author={HAILA AL-ODAN and T. Shaman},
We consider an immersed orientable hypersurface f : M → R of the Euclidean space (f an immersion), and observe that the tangent bundle TM of the hypersurface M is an immersed submanifold of the Euclidean space R. Then we show that in general the induced metric on TM is not a natural metric and obtain expressions for the horizontal and vertical lifts of the vector fields on M . We also study the special case in which the induced metric on TM becomes a natural metric and show that in this case… CONTINUE READING

From This Paper

Topics from this paper.


Publications citing this paper.


Publications referenced by this paper.
Showing 1-8 of 8 references

The fundamental equations of a submersion

  • B. O’Neill
  • Mich. Math. J.,
  • 1966
Highly Influential
6 Excerpts

On the differential geometry of tangent bundles of Riemannian manifolds

  • S. Sasaki
  • Tohoku Math. J.,
  • 1958
Highly Influential
5 Excerpts

On the geometry of the tangent bundle with the Cheeger-Gromoll metric

  • S. Gudmundsson, E. Kappos
  • Tokyo J. Math.,
  • 2002

Locally symmetric space structures on the tangent bundle

  • V. Oproiu, N. Papaghiuc
  • In Differential Geometry and Applications…
  • 1999
1 Excerpt

Curvatures of tangent bundles with Cheeger-Gromoll metric

  • M. Sekizawa
  • Tokyo J. Math.,
  • 1991
1 Excerpt

On the structure of complete manifolds of nonnegative curvature

  • J. Cheeger, D. Gromoll
  • Ann. Math.,
  • 1972
1 Excerpt

Curvature of the induced Riemannian metric on the tangent bundle of a Riemannian manifold

  • O. Kowalski
  • J. Reine Angew. Math.,
  • 1971

Similar Papers

Loading similar papers…