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.
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.
Nakagawa, On differentiable manifolds
with certain almost contact structures, Sci.
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.
We remark that higher order rate distortion manifolds are likely to give better approximations than lower ones, in the same sense that second order tangent structures give better, if more complicated, approximations in conventional differentiable manifolds
We have used differentiable manifolds
through out this paper.
Structures on a differentiable manifolds
and their applications, Chandrama Prakashan, 50-A, Bairampur House, Allahabad, 1984.