**An Introduction to Riemannian Geometry with Applications to Mechanics and Relativity**

by Leonor Godinho, Jose Natario

2004**Number of pages**: 272

**Description**:

Contents: Differentiable Manifolds; Differential Forms; Riemannian Manifolds; Curvature; Geometric Mechanics; Relativity (Galileo Spacetime, Special Relativity, The Cartan Connection, General Relativity, The Schwarzschild Solution).

Download or read it online for free here:

**Download link**

(1.9MB, PDF)

## Similar books

**Complex Analysis on Riemann Surfaces**

by

**Curtis McMullen**-

**Harvard University**

Contents: Maps between Riemann surfaces; Sheaves and analytic continuation; Algebraic functions; Holomorphic and harmonic forms; Cohomology of sheaves; Cohomology on a Riemann surface; Riemann-Roch; Serre duality; Maps to projective space; etc.

(

**14163**views)

**Lectures notes on compact Riemann surfaces**

by

**Bertrand Eynard**-

**arXiv.org**

An introduction to the geometry of compact Riemann surfaces. Contents: Riemann surfaces; Functions and forms on Riemann surfaces; Abel map, Jacobian and Theta function; Riemann-Roch; Moduli spaces; Eigenvector bundles and solutions of Lax equations.

(

**5231**views)

**Holonomy Groups in Riemannian Geometry**

by

**Andrew Clarke, Bianca Santoro**-

**arXiv**

The holonomy group is one of the fundamental analytical objects that one can define on a Riemannian manfold. These notes provide a first introduction to the main general ideas on the study of the holonomy groups of a Riemannian manifold.

(

**8199**views)

**A Sampler of Riemann-Finsler Geometry**

by

**D. Bao, R. Bryant, S. Chern, Z. Shen**-

**Cambridge University Press**

Finsler geometry generalizes Riemannian geometry in the same sense that Banach spaces generalize Hilbert spaces. The contributors consider issues related to volume, geodesics, curvature, complex differential geometry, and parametrized jet bundles.

(

**14008**views)