The best 17 Differential Geometry books

An Introduction to Tensors and Group Theory for Physicists by Nadir Jeevanjee provides a comprehensive and accessible introduction to these important mathematical tools in the field of physics. It covers the fundamental concepts of tensors and group theory, and their applications in various areas of physics. The book is designed to help physicists understand and apply these mathematical concepts in their research and studies.

Applied Differential Geometry by William L. Burke provides a comprehensive introduction to the mathematical framework of differential geometry and its practical applications in various fields such as physics, engineering, and computer graphics. Through clear explanations and real-world examples, the book equips readers with the necessary tools to understand and analyze curved spaces, surfaces, and geometric structures.

Benjamin Harrison by Charles W. Calhoun offers a comprehensive and insightful look at the life and presidency of the 23rd President of the United States. Through meticulous research and engaging writing, Calhoun delves into Harrison's political career, his role in shaping American policies, and his lasting impact on the country. It is a must-read for anyone interested in American history and politics.

Curvature in Mathematics and Physics by Shlomo Sternberg delves into the fascinating concept of curvature and its applications in both mathematics and physics. From the curvature of space-time in general relativity to the curvature of surfaces in differential geometry, this book provides a comprehensive exploration of this fundamental geometric property.

Differential Geometric Structures by Walter A. Poor provides a comprehensive introduction to the fundamental concepts and techniques in differential geometry. It covers topics such as manifolds, curvature, connections, and Riemannian geometry, making it an essential read for anyone interested in the mathematical study of smooth shapes and spaces.

Differential Manifolds by Antoni A. Kosinski provides a comprehensive introduction to the study of differential manifolds. It covers topics such as smooth manifolds, tangent spaces, vector fields, differential forms, and integration on manifolds. With clear explanations and examples, this book is suitable for students and researchers interested in differential geometry and its applications.

Differential Geometry of Curves and Surfaces by Manfredo P. do Carmo is a classic text that provides a comprehensive introduction to the study of curves and surfaces in differential geometry. It covers topics such as curvature, geodesics, and the Gauss-Bonnet theorem, making it an essential read for anyone interested in this field.

First Steps in Differential Geometry by Andrew McInerney provides an accessible introduction to the fundamental concepts of differential geometry. Through clear explanations and illustrative examples, the book covers topics such as curves, surfaces, curvature, and the Gauss-Bonnet theorem. It is a valuable resource for students and anyone interested in exploring the geometric properties of spaces.

Introduction to Differential Geometry of Space Curves and Surfaces by Taha Sochi provides a comprehensive introduction to the fundamental concepts and techniques in the field of differential geometry. It covers topics such as curvature, torsion, geodesics, and the Gauss-Bonnet theorem, offering clear explanations and insightful examples. Whether you're a student or a researcher, this book serves as an invaluable resource for understanding the geometric properties of curves and surfaces in space.

Introduction to Tensor Analysis and the Calculus of Moving Surfaces by Pavel Grinfeld provides a comprehensive introduction to the mathematical concepts of tensor analysis and differential geometry. It covers topics such as vector and tensor algebra, covariant and contravariant tensors, curvature and torsion, and the calculus of moving surfaces. With clear explanations and numerous examples, this book is a valuable resource for students and researchers in the fields of physics, engineering, and mathematics.

Mathematical Discovery on Understanding, Learning, and Teaching Problem Solving, Volume I by George Polya delves into the process of problem solving in mathematics. It provides insights and strategies for understanding and tackling mathematical problems, making it an essential read for students, educators, and anyone interested in the beauty of mathematical discovery.

Synthetic Differential Geometry by Anders Kock explores the foundations of differential geometry using a purely algebraic approach. It introduces the concept of synthetic differential geometry, which provides a framework for studying smooth manifolds and differential equations without relying on the notion of limits. The book delves into the mathematical machinery behind this approach and its applications in various areas of mathematics and physics.

The Absolute Differential Calculus by Tullio Levi-Civita is a groundbreaking mathematical work that delves into the theory of tensors and their applications in differential geometry and physics. Originally published in 1926, this book provides a rigorous treatment of the subject, making it an essential resource for anyone interested in advanced calculus and its role in modern science.

Topology from the Differentiable Viewpoint by John Willard Milnor offers a unique perspective on topology, focusing on differentiable manifolds and smooth maps. It provides a thorough introduction to the subject, covering key concepts such as homotopy, homology, and cohomology. The book is highly regarded for its clear explanations and insightful discussions, making it a valuable resource for students and researchers alike.

Regular Polytopes by H. S. M. Coxeter is a comprehensive exploration of higher-dimensional geometry. Through clear explanations and insightful diagrams, the book delves into the symmetrical properties and characteristics of regular polytopes, providing a deep understanding of these fascinating mathematical structures. It is a must-read for anyone interested in the beauty and complexity of geometric shapes.

Riemannian Manifolds by John M. Lee is a comprehensive introduction to the theory of Riemannian geometry. It covers topics such as curvature, connections, geodesics, and the interplay between geometry and topology. With clear explanations and thorough proofs, this book is a valuable resource for anyone interested in this fascinating branch of mathematics.

The Geometry of Physics by Theodore Frankel explores the deep connections between mathematics and physics. Through the lens of differential geometry and topology, the book delves into the fundamental principles that underlie modern theories of physics, such as general relativity and quantum mechanics. It offers a comprehensive and rigorous treatment of the subject, making it an essential read for anyone interested in the mathematical foundations of theoretical physics.