Differential Geometry

R. A. Sharipov's Course of Differential Geometry PDF

By R. A. Sharipov

ISBN-10: 5747701290

ISBN-13: 9785747701298

Show description

Read Online or Download Course of Differential Geometry PDF

Best differential geometry books

Variational principles for second-order differential - download pdf or read online

During this publication the writer has attempted to use "a little mind's eye and pondering" to modelling dynamical phenomena from a classical atomic and molecular standpoint. Nonlinearity is emphasised, as are phenomena that are elusive from the continuum mechanics perspective. FORTRAN programmes are supplied within the appendices An advent to formal integrability idea of partial differential structures; Frolicher-Nijenhuis conception of derivations; differential algebraic formalism of connections; valuable stipulations for variational sprays; obstructions to the integrability of the Euler-Lagrange process; the type of in the neighborhood variational sprays on two-dimensional manifolds; Euler-Lagrange structures within the isotropic case

An Introduction to Dirac Operators on Manifolds by Jan Cnops PDF

Dirac operators play a tremendous function in numerous domain names of arithmetic and physics, for instance: index conception, elliptic pseudodifferential operators, electromagnetism, particle physics, and the illustration idea of Lie teams. during this primarily self-contained paintings, the fundamental principles underlying the concept that of Dirac operators are explored.

Get L’Hôpital's Analyse des infiniments petits: An Annotated PDF

This monograph is an annotated translation of what's thought of to be the world’s first calculus textbook, initially released in French in 1696. That anonymously released textbook on differential calculus was once in keeping with lectures given to the Marquis de l’Hôpital in 1691-2 via the good Swiss mathematician, Johann Bernoulli.

Extra info for Course of Differential Geometry

Example text

6) ϑ = arccos x3 / ((x1 )2 + (x2 )2 + (x3 )2 ,      ϕ = arctan(x2 /x1 ). Coordinate lines of spherical coordinates form three families. The first family is composed of the rays coming out from the point O; the second family is formed by circles that lie in various vertical planes passing through the axix Ox3 ; and the third family consists of horizontal circles whose centers are on the axis Ox3 . Exactly three coordinate lines pass through each regular point of the space E, one line from each family.

However, for ∇k the special name is reserved, it is called the operator of covariant differentiation or the covariant derivative. Below (in Chapter III) we shall see that the concept of covariant derivative can be extended so that it will not coincide with the partial derivative any more. Let A be a differentiable tensor field of the type (r, s) and let X be some arbitrary vector field. Let’s consider the tensor product ∇A ⊗ X. This is the tensor field of the type (r + 1, s + 1). The covariant differentiation adds one covariant index, while the tensor multiplication add one contravariant index.

Jm−1 n−1 k jn ... js−1 k=1 q=1 ∂xq proves the fifth property. This completes the proof of the theorem in whole. § 6. The metric tensor and the volume pseudotensor. Let O, e1 , e2 , e3 be some Cartesian coordinate system in the space E. The space E is equipped with the scalar product. Therefore, the basis e1 , e2 , e3 of any Cartesian coordinate system has its Gram matrix gij = (ei | ej ). 1) The gram matrix g is positive and non-degenerate: det g > 0. 2) follows from the Silvester criterion (see [1]).

Download PDF sample

Course of Differential Geometry by R. A. Sharipov

by Jeff

Rated 4.68 of 5 – based on 38 votes