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# Tangent Bundle of the Hypersurfaces in a Euclidean Space

@inproceedings{ALODAN2007TangentBO, title={Tangent Bundle of the Hypersurfaces in a Euclidean Space}, author={HAILA AL-ODAN and T. Shaman}, year={2007} }

- Published 2007

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