By S. P. Novikov
The ebook offers the fundamentals of Riemannian geometry in its smooth shape as geometry of differentiable manifolds and an important buildings on them. The authors' technique is that the resource of all structures in Riemannian geometry is a manifold that enables one to compute scalar items of tangent vectors. With this technique, the authors exhibit that Riemannian geometry has an exceptional effect to numerous primary components of contemporary arithmetic and its functions. specifically, Geometry is a bridge among natural arithmetic and traditional sciences, to begin with physics. primary legislation of nature are formulated as relatives among geometric fields describing a number of actual amounts. The research of worldwide houses of geometric items results in the far-reaching improvement of topology, together with topology and geometry of fiber bundles. Geometric thought of Hamiltonian structures, which describe many actual phenomena, ended in the improvement of symplectic and Poisson geometry. box concept and the multidimensional calculus of adaptations, offered within the publication, unify arithmetic with theoretical physics. Geometry of complicated and algebraic manifolds unifies Riemannian geometry with sleek complicated research, in addition to with algebra and quantity thought. necessities for utilizing the publication comprise a number of uncomplicated undergraduate classes, resembling complex calculus, linear algebra, traditional differential equations, and components of topology.
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