
Clifford and RiemannFinsler Structures in Geometric Mechanics a
Author:
S. Vacaru, P. Stavrinos, E. Gaburov, D. Gonta
Language:
The book contains a collection of works on RiemannCartan and metricaffine manifolds provided with nonlinear connection structure and on generalized FinslerLagrange and CartanHamilton geometries an . . . . . 
Natural operations in differential geometry
Author:
Ivan Kolar, Jan Slovak, Peter W. Michor
Language:
The aim of this book is threefold:First it should be a monographical work on natural bundles and natural operators in differential geometry. This is a field which every differential geometer has met s . . . . . 
Topics in Differential Geometry
Author:
Peter W. Michor
Language:
Contents: Manifolds and Vector Fields; Lie Groups; Diﬀerential Forms and De Rham Cohomology; Riemannian Geometry; Bundles and Connections; Symplectic Geometry and Hamiltonian Mechanics.

Introduction to Tensor Calculus and Continuum Mechanics
Author:
John H. Heinbockel
Language:
 Introduction to Tensor Calculus and Continuum Mechanics is an advanced College level mathematics text. The first part of the text introduces basic concepts, notations and operations associated with th . . . . . 

Invariance Theory, The Heat Equation, The ATIYAHSINGER Theo
Author:
Peter B. Gilkey
Language:
Contents: PseudoDifferential Operators; Characteristic Classes; The Index Theorem; Generalized Index Theorems and Special Topics. 
Projective dierential geometry old and new: from Schwarzian derivative to cohomology of dieomorphism groups
Author:
V. Ovsienko and S. Tabachnikov
Language:
This book is not an exhaustive introduction to projective dierential
geometry or a survey of its recent developments. It is addressed to the
reader who wishes to cover a greater distance in a short . . . . . 
Geometric Wave Equations
Author:
Stefan Waldmann
Language:
In these lecture notes we discuss the solution theory of geometric wave equations as they arise in Lorentzian geometry: for a normally hyperbolic differential operator the existence and uniqueness pro . . . . . 
Riemannian Submanifolds: A Survey
Author:
BangYen Chen
Language:
Submanifold theory is a very active vast research field which plays an important role in the development of modern differential geometry. This branch of differential geometry is still so far from . . . . . 
Notes on dierential geometry
Author:
Matt Visser
Language:
In this course I will present an overview of differential geometry, also known as the theory of manifolds, (sometimes loosely known as nonEuclidean geometry or Riemannian
geometry, but that is actu . . . . . 
Synthetic Differential Geometry
Author:
Anders Kock
Language:
Contents: The synthetic theory; Categorical logic; Models. 
Lectures on Differential Geometry
Author:
Wulf Rossmann
Language:
 Contents:Chapter 1. Manifolds
1.1 Review of calculus
1.2 Manifolds:definitions and examples
1.3 Vectors and differentials
1.4 Submanifolds
1.5 Riemann metrics
Chapter 2. Tensor Calcu . . . . . 

Notes on Differential Geometry
Author:
Hicks
Language:
Contents: Manifolds; hypersurfaces of Rn; surfaces in R3; Tensors and forms; connexions; rienmann manifolds and submanifolds; operators on forms and integration; gaussbonnet theory of rigidity; exist . . . . . 
Riemannian manifolds with geometric structures
Author:
Alexander A. Ermolitsky
Language:
Some geometric structures with associated Riemannian metrics have been considered in the book. 
Projective and Polar Spaces
Author:
Peter J. Cameron
Language:
 Contents: 1. Projective spaces; 2. Projective planes; 3. Coordinatisation of projective spaces; 4. Various topics; 5. Buekenhout geometries; 6. Polar spaces; 7. Axioms for polar spaces; 8. The Klein . . . . . 

Riemann Surfaces, Dynamics and Geometry
Author:
C. McMullen
Language:
 Contents: Introduction; Geometric function theory; Teichm¨uller theory; Teichm¨uller theory; Teichm¨uller theory; Holomorphic motions and structural stability; Iteration on Teichm¨uller space; Geometr . . . . . 

Course of differential geometry
Author:
Ruslan Sharipov
Language:
This book is a textbook for the basic course of differential geometry. It is recommended as an introductory material for this subject. 
RicciHamilton flow on surfaces: lectures on works of R.Hamilton and G.Perelman
Author:
Li Ma
Language:
Contents: RicciHamilton flow on surfaces; BartzStruweYe estimate; Hamilton’s another proof on S^2; Perelman’s Wfunctional and its applications; Appendix A: RicciHamilton flow on Riemannian manifo . . . . . 
Differential Geometry: A First Course in Curves and Surfaces
Author:
Theodore Shifrin
Language:
Contents: CURVES; SURFACES: LOCAL THEORY; SURFACES: FURTHER TOPICS; REVIEW OF LINEAR ALGEBRA AND CALCULUS; SOLUTIONS TO SELECTED EXERCISES. 
Lectures on Differential Geometry
Author:
Werner Ballmann
Language:
Contents: Basic Geometry of Submanifolds; Connections and Geodesics; Vector Bundles and Connections; SemiRiemannian Metrics; Riemannian Immersions and Submersions; Variational Theory of Geodesic . . . . . 
Differentiable Manifolds
Author:
Nigel Hitchin
Language:
Contents: Introduction; Manifolds; Tangent vectors and cotangent vectors; Vector fields; Tensor products; Differential forms; Integration of forms; The degree of a smooth map; Riemannian metrics; appe . . . . . 
Topics in Differential Geometry
Author:
Werner Ballman
Language:
Contents: On the Geometry of Metric Spaces; Automorphism Groups; Geometric Structures; Homogeneous Structures; Symmetric Spaces. 
Introduction to evolution equations in geometry
Author:
Bianca Santoro
Language:
These are the very unpretentious lecture notes for the minicourse "Introduction to evolution equations in Geometry," a part of the Brazilian Colloquium of Mathematics held at IMPA, in July of 2009. 
Noncompact harmonic manifolds
Author:
Gerhard Knieper, Norbert Peyerimhoff
Language:
The Lichnerowicz conjecture asserts that all harmonic manifolds are either flat or locally symmetric spaces of rank 1. This conjecture has been proved by Z.I. Szabo for harmonic manifolds with compact . . . . . 
A Course in Riemannian Geometry
Author:
Dr. David R. Wilkins
Language:
Contents: Smooth Manifolds; Tangent Spaces ; Affine Connections on Smooth Manifolds; Riemannian Manifolds; Geometry of Surfaces in R3; Geodesics in Riemannian Manifolds; Complete Riemannian Manifolds; . . . . . 
Orthonormal Basis in Minkowski Space
Author:
Aleks Kleyn, Alexandre Laugier
Language:
Finsler space is differentiable manifold for which Minkowski space is the fiber of the tangent bundle. To understand structure of the reference frame in Finsler space, we need to understand the struct . . . . . 
Notes on Differential Geometry
Author:
Markus Deserno
Language:
These notes are an attempt to summarize some of the key mathematical
aspects of differential geometry, as they apply in particular
to the geometry of surfaces in R3. The focus is not on mathematical . . . . . 
Lecture Notes on Differential Geometry
Author:
Alexander Altland
Language:
Contents: Exterior Calculus; Manifolds; Lie groups; Fibre bundles. 
Differential Geometry and Physics
Author:
Gabriel Lugo
Language:
Contents:
I. Vectors and Curves
1.1 Tangent Vectors
1.2 Curves
1.3 Fundamental Theorem of Curves II. Differential forms
2.1 1Forms
2.2 Tensors and Forms of Higher Rank
2.3 Exterior Derivativ . . . . . 
Lectures on CalabiYau and special Lagrangian geometry
Author:
Dominic Joyce
Language:
This paper gives a leisurely introduction to CalabiYau manifolds and special Lagrangian submanifolds from the differential geometric point of view, followed by a survey of recent results on singulari . . . . . 
A primer on the (2 1) Einstein universe
Author:
Thierry Barbot, Virginie Charette, Todd Drumm, William M. Goldma
Language:
The Einstein universe is the conformal compactification of Minkowski space. It also arises as the ideal boundary of antide Sitter space. The purpose of this article is to develop the synthetic ge . . . . . 
Diffential Geometry: Lecture Notes
Author:
Dimitri Zaitev
Language:
Contents: Introduction to smooth manifolds; basic results from differential topology; tangent spaces and tensor calculus; Riemannian geometry. 
Lectures on Minimal Surface Theory
Author:
Brian White
Language:
An article based on a fourlecture introductory minicourse on minimal surface theory given at the 2013 summer program of the Institute for Advanced Study and the Park City Mathematics Institute. 
Lecture notes for the course in Differential Geometry
Author:
Yakov
Language:
Mostly they constitute a collection of definitions, formulations of most important theorems and related problems for selfcontrol. 
Differential Geometry
Author:
Balázs Csikós
Language:
Basic Structures on Rn; Curvatures of a Curve; 3D Curves  Curves on Hypersurfaces; Hypersurfaces; Surfaces in the 3dimensional space;
Surfaces in the 3dimensional space; The Lie Algebra of Vector . . . . . 
Introduction aux variétés différentielles
Author:
Jacques Lafontaine
Language:
 Contenu: Prérequis en topologie; Calcul différentiel; Notions de base sur les variétés; Du local au global; Autour des groupes de Lie; Formes différentielles; Intégration et applications; Cohomologie . . . . . 
