The notion of slant submanifold was generalized by semislant submanifold, pseudo-slant submanifold, and bi-slant submanifold, respectively, in different types of differentiable manifolds
. The semi-slant submanifold of almost Hermitian manifold was introduced by N.
Spadini, On the uniqueness of the fixed point index on differentiable manifolds
, Fixed Point Theory Appl., 2004:4, 251-259.
They cover differentiable manifolds
, Finsler metrics, connections and curvatures, S-curvature, Riemann curvature, projective changes, comparison theorems, fundamental groups of Finsler manifolds, minimal immersions and harmonic maps, Einstein metrics, and miscellaneous topics.
Boothby, Introduction to Differentiable Manifolds
and Riemannian Geometry, Academic Press, Orlando, Fla, USA, 2nd edition, 2002.
An n-dimensional differentiable manifolds
[M.sup.n] is a Lorentzian Para-Sasakian manifolds(briefly LP-Sasakian manifolds) if it admits a (1,1) tensor field [phi], contravariant vector field [xi], a covariant vector field [eta], and a Lorentzian metric g, which satisfy
Our approach is based on the following sampling existence theorem for differentiable manifolds
that was recently presented and applied in the context of Image Processing (, ) (1):
Indeed, let N and M be two differentiable manifolds
and x: N [right arrow] M be a differentiable submanifold map.
The textbook is for graduate students who are interested in analysis and geometry and have completed basic first courses in real and complex analysis, differentiable manifolds
, and topology.
Tangent bundles of differentiable manifolds
are of great importance in many areas of mathematics and physics.
His dissertation was entitled Substructure of Differentiable Manifolds
and Riemannian Spaces with Singularities.
 Colon, L., 1983, Differentiable Manifolds
, Basel: Birkhauser.
This text for graduate students and research mathematicians progresses from differentiable manifolds
and the tangent structure through the local Frobenius theorem, covariant derivatives, and Riemannian and semi-Riemannian geometry.