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by Richard L. Bishop - arXiv , 2013
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.
An Introduction to Riemannian Geometry with Applications to Mechanics and Relativity
by Leonor Godinho, Jose Natario , 2004
Contents: Differentiable Manifolds; Differential Forms; Riemannian Manifolds; Curvature; Geometric Mechanics; Relativity (Galileo Spacetime, Special Relativity, The Cartan Connection, General Relativity, The Schwarzschild Solution).
Holonomy Groups in Riemannian Geometry
by Andrew Clarke, Bianca Santoro - arXiv , 2012
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.
Lectures on Geodesics in Riemannian Geometry
by M. Berger - Tata Institute of Fundamental Research , 1965
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.
Medians and Means in Riemannian Geometry: Existence, Uniqueness and Computation
by M. Arnaudon, F. Barbaresco, L. Yang - arXiv , 2011
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.
A Course in Riemannian Geometry
by David R. Wilkins - Trinity College, Dublin , 2005
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.
Lectures on Differential Geometry
by John Douglas Moore - University of California , 2009
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.
A Panoramic View of Riemannian Geometry
by Marcel Berger - Springer , 2002
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.
Complex Analysis on Riemann Surfaces
by Curtis McMullen - Harvard University , 2005
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.
A Sampler of Riemann-Finsler Geometry
by D. Bao, R. Bryant, S. Chern, Z. Shen - Cambridge University Press , 2004
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.
Riemann Surfaces, Dynamics and Geometry
by Curtis McMullen - Harvard University , 2008
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.
An Introduction to Riemannian Geometry
by Sigmundur Gudmundsson - Lund University , 2010
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.
Semi-Riemann Geometry and General Relativity
by Shlomo Sternberg , 2003
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.