## e-books in Introductory Differential Geometry category

**Differential Geometry: A Geometric Introduction**

by

**David W. Henderson**-

**Project Euclid**,

**2013**

This is the only book that introduces differential geometry through a combination of an intuitive geometric foundation, a rigorous connection with the standard formalisms, computer exercises with Maple, and a problems-based approach.

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**2248**views)

**Differential Geometry Of Three Dimensions**

by

**C.E. Weatherburn**-

**Cambridge University Press**,

**1955**

The book is devoted to differential invariants for a surface and their applications. By the use of vector methods the presentation is both simplified and condensed, and students are encouraged to reason geometrically rather than analytically.

(

**6787**views)

**A Course Of Differential Geometry**

by

**John Edward Campbell**-

**Clarendon Press**,

**1926**

Contents: Tensor theory; The ground form when n=2; Geodesics in two-way space; Two-way space as a locus in Euclidean space; Deformation of a surface and congruences; Curves in Euclidean space and on a surface; The ruled surface; Minimal surface; etc.

(

**4336**views)

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

by

**Theodore Shifrin**-

**University of Georgia**,

**2015**

Contents: Curves (Examples, Arclength Parametrization, Frenet Frame); Surfaces: Local Theory (Parametrized Surfaces, Gauss Map, Covariant Differentiation, Parallel Translation, Geodesics); Surfaces: Further Topics (Holonomy, Hyperbolic Geometry,...).

(

**5512**views)

**Differential Geometry: Lecture Notes**

by

**Dmitri Zaitsev**-

**Trinity College Dublin**,

**2004**

From the table of contents: Chapter 1. Introduction to Smooth Manifolds; Chapter 2. Basic results from Differential Topology; Chapter 3. Tangent spaces and tensor calculus; Tensors and differential forms; Chapter 4. Riemannian geometry.

(

**9325**views)

**Lectures on Differential Geometry**

by

**Wulf Rossmann**-

**University of Ottawa**,

**2003**

This is a collection of lecture notes which the author put together while teaching courses on manifolds, tensor analysis, and differential geometry. He offers them to you in the hope that they may help you, and to complement the lectures.

(

**9421**views)

**Differential Geometry**

by

**Balazs Csikos**-

**Eötvös Loránd University**,

**2010**

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.

(

**10193**views)

**Differential Geometry Course Notes**

by

**Richard Koch**-

**University of Oregon**,

**2005**

These are differential geometry course notes. From the table of contents: Preface; Curves; Surfaces; Extrinsic Theory; The Covariant Derivative; The Theorema Egregium; The Gauss-Bonnet Theorem; Riemann's Counting Argument.

(

**9559**views)

**Elementary Differential Geometry**

by

**Gilbert Weinstein**-

**UAB**,

**2009**

These notes are for a beginning graduate level course in differential geometry. It is assumed that this is the students' first course in the subject. Thus the choice of subjects and presentation has been made to facilitate a concrete picture.

(

**11027**views)

**Topics in Differential Geometry**

by

**Peter W. Michor**-

**American Mathematical Society**,

**2008**

Fundamentals of differential geometry: manifolds, flows, Lie groups and their actions, invariant theory, differential forms and de Rham cohomology, bundles and connections, Riemann manifolds, isometric actions, and symplectic and Poisson geometry.

(

**9292**views)

**Notes on Differential Geometry**

by

**Noel J. Hicks**-

**Van Nostrand**,

**1965**

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.

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**11642**views)

**Differential Geometry in Physics**

by

**Gabriel Lugo**-

**University of North Carolina at Wilmington**,

**2006**

These notes were developed as a supplement to a course on Differential Geometry at the advanced undergraduate level, which the author has taught. This texts has an early introduction to differential forms and their applications to Physics.

(

**15655**views)

**Course of Differential Geometry**

by

**Ruslan Sharipov**-

**Samizdat Press**,

**2004**

Textbook for the first course of differential geometry. It covers the theory of curves in three-dimensional Euclidean space, the vectorial analysis both in Cartesian and curvilinear coordinates, and the theory of surfaces in the space E.

(

**13582**views)

**Introduction to Differential Geometry and General Relativity**

by

**Stefan Waner**,

**2005**

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.

(

**19480**views)

**Differentiable Manifolds**

by

**Nigel Hitchin**,

**2003**

The historical driving force of the theory of manifolds was General Relativity, where the manifold is four-dimensional spacetime, wormholes and all. This text is occupied with the theory of differential forms and the exterior derivative.

(

**15871**views)

**Tensor Analysis**

by

**Edward Nelson**-

**Princeton Univ Pr**,

**1974**

The lecture notes for the first part of a one-term course on differential geometry given at Princeton in the spring of 1967. They are an expository account of the formal algebraic aspects of tensor analysis using both modern and classical notations.

(

**16604**views)