## e-books in Riemannian Geometry category

**Treatise on Differential Geometry and its role in Relativity Theory**

by

**Subenoy Chakraborty**-

**arXiv.org**,

**2022**

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.

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**3086**views)

**Lectures notes on compact Riemann surfaces**

by

**Bertrand Eynard**-

**arXiv.org**,

**2018**

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.

(

**5398**views)

**Riemannian Geometry: Definitions, Pictures, and Results**

by

**Adam Marsh**-

**arXiv**,

**2014**

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.

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**6889**views)

**Riemannian Submanifolds: A Survey**

by

**Bang-Yen Chen**-

**arXiv**,

**2013**

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.

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**7155**views)

**Riemannian Geometry**

by

**Ilkka Holopainen, Tuomas Sahlsten**,

**2013**

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.

(

**8646**views)

**Riemannian Geometry**

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.

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**9885**views)

**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).

(

**9150**views)

**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.

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**8352**views)

**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.

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**9555**views)

**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.

(

**10073**views)

**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.

(

**11653**views)

**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.

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**11422**views)

**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.

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**12124**views)

**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.

(

**14388**views)

**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.

(

**14189**views)

**Riemann Surfaces, Dynamics and Geometry**

by

**Curtis McMullen**-

**Harvard University**,

**2020**

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.

(

**14510**views)

**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.

(

**14360**views)

**Semi-Riemann Geometry and General Relativity**

by

**Shlomo Sternberg**,

**2003**

Course notes for an introduction to Riemannian geometry and its principal physical application, Einsteinâ€™s theory of general relativity. The background assumed is a good grounding in linear algebra and in advanced calculus.

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**18486**views)