**Riemannian Geometry**

by Ilkka Holopainen, Tuomas Sahlsten

2013**Number of pages**: 102

**Description**:

Based on the lecture notes on differential geometry. From the table of contents: Differentiable manifolds, a brief review; Riemannian metrics; Connections; Geodesics; Curvature; Jacobi fields; Curvature and topology; Comparison geometry; The sphere theorem.

Download or read it online for free here:

**Download link**

(1.3MB, PDF)

## Similar books

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

by

**Leonor Godinho, Jose Natario**

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

(

**5316**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.

(

**10086**views)

**Semi-Riemann Geometry and General Relativity**

by

**Shlomo Sternberg**

Course notes for an introduction to Riemannian geometry and its principal physical application, Einsteinâ€™s theory of general relativity. The background assumed is a good grounding in linear algebra and in advanced calculus.

(

**14254**views)

**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.

(

**10578**views)