**Differential Geometry: A First Course in Curves and Surfaces**

by Theodore Shifrin

**Publisher**: University of Georgia 2015**Number of pages**: 127

**Description**:

Contents: Curves (Examples, Arclength Parametrization, Local Theory: Frenet Frame, Some Global Results), Surfaces: Local Theory (Parametrized Surfaces and the First Fundamental Form, The Gauss Map and the Second Fundamental Form, The Codazzi and Gauss Equations, Covariant Differentiation, Parallel Translation, and Geodesics) Surfaces: Further Topics (Holonomy and the Gauss-Bonnet Theorem, Hyperbolic Geometry, Surface Theory with Differential Forms, Calculus of Variations and Surfaces of Constant Mean Curvature).

Download or read it online for free here:

**Download link**

(1.8MB, PDF)

## Similar books

**Differential Geometry**

by

**Balazs Csikos**-

**Eötvös Loránd University**

Contents: Basic Structures on Rn, Length of Curves; Curvatures of a Curve; Plane Curves; 3D Curves; Hypersurfaces; Surfaces in 3-dimensional space; Fundamental equations of hypersurface theory; Topological and Differentiable Manifolds; etc.

(

**7115**views)

**Notes on Differential Geometry**

by

**Matt Visser**-

**Victoria University of Wellington**

In this text the author presents an overview of differential geometry. Topics covered: Topological Manifolds and differentiable structure; Tangent and cotangent spaces; Fibre bundles; Geodesics and connexions; Riemann curvature; etc.

(

**5306**views)

**Notes on Differential Geometry**

by

**Noel J. Hicks**-

**Van Nostrand**

A concise introduction to differential geometry. The ten chapters of Hicks' book contain most of the mathematics that has become the standard background for not only differential geometry, but also much of modern theoretical physics and cosmology.

(

**7498**views)

**Introduction to Differential Geometry and General Relativity**

by

**Stefan Waner**

Smooth manifolds and scalar fields, tangent vectors, contravariant and covariant vector fields, tensor fields, Riemannian manifolds, locally Minkowskian manifolds, covariant differentiation, the Riemann curvature tensor, premises of general relativity.

(

**15589**views)