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Riemannian Geometry

e-books in Riemannian Geometry category

Book cover: Riemannian GeometryRiemannian Geometry
by - Princeton University Press ,
The recent physical interpretation of intrinsic differential geometry of spaces has stimulated the study of this subject. Throughout the book constant use is made of the methods of tensor analysis and the Absolute Calculus of Ricci and Levi-Civita.
(628 views)
Book cover: Riemannian Geometry: Definitions, Pictures, and ResultsRiemannian Geometry: Definitions, Pictures, and Results
by - arXiv ,
A pedagogical but concise overview of Riemannian geometry is provided in the context of usage in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions and relevant theorems.
(1176 views)

Book cover: Riemannian Submanifolds: A SurveyRiemannian Submanifolds: A Survey
by - arXiv ,
Submanifold theory is a very active vast research field which plays an important role in the development of modern differential geometry. In this book, the author provides a broad review of Riemannian submanifolds in differential geometry.
(2393 views)
Book cover: Riemannian GeometryRiemannian Geometry
by ,
Based on the lecture notes on differential geometry. From the contents: Differentiable manifolds, a brief review; Riemannian metrics; Connections; Geodesics; Curvature; Jacobi fields; Curvature and topology; Comparison geometry; The sphere theorem.
(2682 views)
Book cover: Riemannian GeometryRiemannian Geometry
by - arXiv ,
These notes on Riemannian geometry use the bases bundle and frame bundle, as in Geometry of Manifolds, to express the geometric structures. It starts with the definition of Riemannian and semi-Riemannian structures on manifolds.
(2833 views)
Book cover: Holonomy Groups in Riemannian GeometryHolonomy Groups in Riemannian Geometry
by - arXiv ,
The holonomy group is one of the fundamental analytical objects that one can define on a Riemannian manfold. These notes provide a first introduction to the main general ideas on the study of the holonomy groups of a Riemannian manifold.
(3431 views)
Book cover: Lectures on Geodesics in Riemannian GeometryLectures on Geodesics in Riemannian Geometry
by - Tata Institute of Fundamental Research ,
The main topic of these notes is geodesics. Our aim is to give a fairly complete treatment of the foundations of Riemannian geometry and to give global results for Riemannian manifolds which are subject to geometric conditions of various types.
(4119 views)
Book cover: Medians and Means in Riemannian Geometry: Existence, Uniqueness and ComputationMedians and Means in Riemannian Geometry: Existence, Uniqueness and Computation
by - arXiv ,
This paper is a short summary of our recent work on the medians and means of probability measures in Riemannian manifolds. The existence and uniqueness results of local medians are given. We propose a subgradient algorithm and prove its convergence.
(4903 views)
Book cover: A Course in Riemannian GeometryA Course in Riemannian Geometry
by - Trinity College, Dublin ,
From the table of contents: Smooth Manifolds; Tangent Spaces; Affine Connections on Smooth Manifolds; Riemannian Manifolds; Geometry of Surfaces in R3; Geodesics in Riemannian Manifolds; Complete Riemannian Manifolds; Jacobi Fields.
(5937 views)
Book cover: Lectures on Differential GeometryLectures on Differential Geometry
by - University of California ,
Foundations of Riemannian geometry, including geodesics and curvature, as well as connections in vector bundles, and then go on to discuss the relationships between curvature and topology. Topology will presented in two dual contrasting forms.
(5422 views)
Book cover: A Panoramic View of Riemannian GeometryA Panoramic View of Riemannian Geometry
by - Springer ,
In this monumental work, Marcel Berger manages to survey large parts of present day Riemannian geometry. The book offers a great opportunity to get a first impression of some part of Riemannian geometry, together with hints for further reading.
(6029 views)
Book cover: Complex Analysis on Riemann SurfacesComplex Analysis on Riemann Surfaces
by - 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.
(8300 views)
Book cover: A Sampler of Riemann-Finsler GeometryA Sampler of Riemann-Finsler Geometry
by - 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.
(8134 views)
Book cover: Riemann Surfaces, Dynamics and GeometryRiemann Surfaces, Dynamics and Geometry
by - Harvard University ,
This course will concern the interaction between: hyperbolic geometry in dimensions 2 and 3, the dynamics of iterated rational maps, and the theory of Riemann surfaces and their deformations. Intended for advanced graduate students.
(8679 views)
Book cover: An Introduction to Riemannian GeometryAn Introduction to Riemannian Geometry
by - Lund University ,
The main purpose of these lecture notes is to introduce the beautiful theory of Riemannian Geometry. Of special interest are the classical Lie groups allowing concrete calculations of many of the abstract notions on the menu.
(8692 views)
Book cover: Semi-Riemann Geometry and General RelativitySemi-Riemann Geometry and General Relativity
by ,
Course notes for an introduction to Riemannian geometry and its principal physical application, Einstein’s theory of general relativity. The background assumed is a good grounding in linear algebra and in advanced calculus.
(11659 views)