We use the fact that the tangent bundleTMof an orientable hypersurfaceMin the Euclidean spaceRn+1is a submanifold of the Euclidean spaceR2n+2, and use the induced metric onTMas submanifold to study its geometry. This induced metric is not a natural metric in the sense that the projectionπ...
Let (M 3 ,α) be three-dimensional compact orientable manifold without boundary and let α be a contact form on M 3 . Let v be a nonzero vector field in Kerα and let ξ be the Reeb vector field of α. If β=dα(v,·) is a contact form w... A Bahri - 《Palestine Journal...
(\mathcal{E})$, while it is free for $d=2$.For comparison, we also compute the stable cohomology group with coefficients in the $d^{th}$ exterior powers of the first rational cohomology of the unit tangent bundle of the surface, which fit into the classical framework of cohomological ...
The tangent bundle TM of a semi-Riemannian manifold (M, g) admits a natural indefinite almost Kaehler structure (J, G) and the unit tangent hyperquadric bundle \\\(T_{\\\varepsilon } (M,g)\\\), \\\({\\\varepsilon }=\\\pm 1\\\), is an orientable nondegenerate hypersurface ...