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Course of differential geometry
This book contains below topics, CHAPTER CUR VES IN THREEDIMENSIONAL SPACE, The length integral and the natural parametrization of a c urve, Curves as trajectories of material points in mechanics, CHAPTER ELEMENTS OF VECTORIAL AND TENSORIAL ANALYSIS, Vectorial and tensorial elds in the space, Tensor product and contraction, The algebra of tensor elds, Symmetrization and alternation, Dierentiation of tensor elds, The metric tensor and the volume pseudotensor, The properties of pseudotensors.
Author(s): Ruslan Sharipov
132 Pages
Principles of Differential Geometry
The present text is a collection of notes about differential geometry prepared to some extent as part of tutorials about topics and applications related to tensor calculus. This book contains below topics, Preliminaries, Curves in Space, Surfaces in Space, Curvature, Special Types of Curve, Special Types of Surface, Tensor Differentiation.
Author(s): Taha Sochi
161 Pages
This note contains below topics, Preliminaries Sets Maps and Diagrams, Groups, Manifolds, Lie Groups, Some Classical Examples of Lie Groups, Medical Applications Prediction of Injuries.
Author(s): Vladimir G. Ivancevic, Tijana T. Ivancevic
74 Pages
Discrete Differential Geometry
This note covers the following topics, Discrete Curves, Curves and curvature, Flows on curves, Elastica, Darboux transforms, Discrete Surfaces, Abstract discrete surfaces, Polyhedral surfaces and piecewise flat surfaces, Discrete cotan Laplace operator, Delaunay tessellations, Line congruences over simplicial surfaces, Polyhedral surfaces with parallel Gauss map, Willmore energy.
Author(s): Alexander I. Bobenko
144 Pages
Elementary Differential Geometry Curves and Surfaces
The purpose of this course note is the study of curves and surfaces, and those are in general, curved. The book mainly focus on geometric aspects of methods borrowed from linear algebra, proofs will only be included for those properties that are important for the future development.
Author(s): Asst. Prof. Martin Raussen
160 Pages
Differential Geometry Of Three Dimensions
This book describes the fundamentals of metric differential geometry of curves and surfaces.
Author(s): C. E Weatherburn
280 Pages
Lectures on Symplectic Geometry
This note contains below topics, Symplectic Manifolds, Symplectomorphisms, Local Forms, Contact Manifolds, Compatible Almost Complex Structures, Kahler Manifolds, Hamiltonian Mechanics, Moment Maps, Symplectic Reduction, Moment Maps Revisited and Symplectic Toric Manifolds.
Author(s): Ana Cannas da Silva
225 Pages
Notes on Differential Geometry and Lie Groups
This note covers the following topics, Matrix Exponential, Some Matrix Lie Groups, Manifolds and Lie Groups, The Lorentz Groups, Vector Fields, Integral Curves, Flows, Partitions of Unity, Orientability, Covering Maps, The LogEuclidean Framework, Spherical Harmonics, Statistics on Riemannian Manifolds, Distributions and the Frobenius Theorem, The LaplaceBeltrami Operator and Harmonic Forms, Bundles, Metrics on Bundles, Homogeneous Spaces, Cli ord Algebras, Cli ord Groups, Pin and Spin and Tensor Algebras.
Author(s): Jean Gallier
744 Pages
