 # Riemannian Geometry

## e-books in Riemannian Geometry category Treatise on Differential Geometry and its role in Relativity Theory
by - arXiv.org ,
These notes will be helpful to undergraduate and postgraduate students in theoretical physics and in applied mathematics. Modern terminology in differential geometry has been discussed in the book with the motivation of geometrical way of thinking.
(1056 views) Lectures notes on compact Riemann surfaces
by - arXiv.org ,
An introduction to the geometry of compact Riemann surfaces. Contents: Riemann surfaces; Functions and forms on Riemann surfaces; Abel map, Jacobian and Theta function; Riemann-Roch; Moduli spaces; Eigenvector bundles and solutions of Lax equations.
(3878 views) Riemannian 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.
(5368 views) Riemannian 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.
(5859 views) Riemannian 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.
(7060 views) Riemannian 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.
(7945 views) An Introduction to Riemannian Geometry with Applications to Mechanics and Relativity
by ,
Contents: Differentiable Manifolds; Differential Forms; Riemannian Manifolds; Curvature; Geometric Mechanics; Relativity (Galileo Spacetime, Special Relativity, The Cartan Connection, General Relativity, The Schwarzschild Solution).
(7671 views) Holonomy 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.
(7066 views) Lectures 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.
(8014 views) Medians 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.
(8577 views) A 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.
(10054 views) Lectures 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.
(9706 views) A 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.
(10530 views) Complex 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.
(12633 views) A 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.
(12387 views) Riemann 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.
(12820 views) An 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.
(12737 views) Semi-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.
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