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Definitive Collection: Differential & Riemannian Geometry

Javier Álvarez "Empiricist"
 
Elementary Differential Geometry (Springer Undergraduate Mathematics Series)
Elementary Differential Geometry (Springer Undergraduate Mathematics Series)
Elementary Differential Geometry
Elementary Differential Geometry
Lectures on Classical Differential Geometry: Second Edition (Dover Books on Mathematics)
Lectures on Classical Differential Geometry: Second Edition (Dover Books on Mathematics)
Differential Geometry (Dover Books on Mathematics)
Differential Geometry (Dover Books on Mathematics)
"Classic (old-fashioned) treatment of the differential geometry of curves and surfaces. From Frenet-Serret to fundamental forms and Gauß-Bonnet theorem."
Differential Geometry of Curves and Surfaces: A Concise Guide
Differential Geometry of Curves and Surfaces: A Concise Guide
"Modern classical introduction to the differential geometry of curves and surfaces, focusing on interesting properties and geometric results, rather than development of the general theory."
Differential Geometry: Curves - Surfaces - Manifolds, Second Edition
Differential Geometry: Curves - Surfaces - Manifolds, Second Edition
"Complementing the previous title, Kühnel develops differential geometry of manifolds from the motivation of curves and surfaces, up to covariant derivatives and Riemannian geometry."
Curves and Surfaces (UNITEXT / La Matematica per il 3+2)
Curves and Surfaces (UNITEXT / La Matematica per il 3+2)
"A new modern title able to become a standard reference at the level of do Carmo. Deep development of the abstract theory and all major results."
Differential Geometry: Manifolds, Curves, and Surfaces (Graduate Texts in Mathematics)
Differential Geometry: Manifolds, Curves, and Surfaces (Graduate Texts in Mathematics)
Differential Geometry of Curves and Surfaces
Differential Geometry of Curves and Surfaces
"The classic standard references on differential curves and surfaces, both local and global treatments."
Metric Structures in Differential Geometry (Graduate Texts in Mathematics)
Metric Structures in Differential Geometry (Graduate Texts in Mathematics)
"Short but advanced rigorous introduction to a broad selection of topics. Very instructive lectures to get a formal overview of the whole subject."
Manifolds and Differential Geometry (Graduate Studies in Mathematics)
Manifolds and Differential Geometry (Graduate Studies in Mathematics)
"Comprehensive advanced introduction to manifolds, with a thorough treatment of every fundamental topic, from tensors and differential forms, to connections and curvature of fiber bundles, through Riemannian geometry."
Lectures On The Geometry Of Manifolds
Lectures On The Geometry Of Manifolds
"Specially suitable for anyone tending to global analysis. Formal and advanced but very didactic and insightful, with many examples an exercises.  He manages to cover many topics in great detail. The last chapters are unique making it an ideal reading before attempting titles on Dirac operators, spin geometry and index theorems."
Topics in Differential Geometry (Graduate Studies in Mathematics)
Topics in Differential Geometry (Graduate Studies in Mathematics)
"GREAT highly advanced, formal and algebraic treatment of differential geometry, with an emphasis on functoriality and naturality in the differential categories. Very detailed and comprehensive results on many topics at a very general level, and with a growing web supplement pdf."
Foundations of Differential Geometry, Vol.1 (Wiley Classics Library)
Foundations of Differential Geometry, Vol.1 (Wiley Classics Library)
"These two volumes are the classical monographic reference on differential geometry. They cover almost any important topic, and are one of the few book references where the Newlander-Nirenberg theorem is explicitly proved (at least for the analytic case)."
Foundations of Differential Geometry, Vol. 2
Foundations of Differential Geometry, Vol. 2
"Idem as before."
Riemannian Manifolds: An Introduction to Curvature (Graduate Texts in Mathematics)
Riemannian Manifolds: An Introduction to Curvature (Graduate Texts in Mathematics)
"Continuation of the previous books, now bestowing geometry over differentiable manifolds. All three books have become standard textbooks at many graduate schools for these topics."
Riemannian Geometry (Graduate Texts in Mathematics, Vol. 171)
Riemannian Geometry (Graduate Texts in Mathematics, Vol. 171)
"Beautiful and geometric oriented monograph. One of the standard references on advanced Riemannian manifolds."
Riemannian Geometry and Geometric Analysis (Universitext)
Riemannian Geometry and Geometric Analysis (Universitext)
"A true gem for geometric and global analysis. It treats the real and complex aspects from the beginning (review connections and curvature), fundamental development of Hodge theory and with even an introduction to Seiberg-Witten theory."
Riemannian Geometry
Riemannian Geometry
"One of the classic references on the subject."
Riemannian Geometry: A Modern Introduction (Cambridge Studies in Advanced Mathematics)
Riemannian Geometry: A Modern Introduction (Cambridge Studies in Advanced Mathematics)
Semi-Riemannian Geometry With Applications to Relativity, 103, Volume 103 (Pure and Applied Mathematics)
Semi-Riemannian Geometry With Applications to Relativity, 103, Volume 103 (Pure and Applied Mathematics)
Riemannian Holonomy Groups and Calibrated Geometry (Oxford Graduate Texts in Mathematics)
Riemannian Holonomy Groups and Calibrated Geometry (Oxford Graduate Texts in Mathematics)
Differential Geometry, Lie Groups, and Symmetric Spaces (Graduate Studies in Mathematics)
Differential Geometry, Lie Groups, and Symmetric Spaces (Graduate Studies in Mathematics)
"Standard monographic reference on homogeneous and symmetric spaces. It review Riemannian geometry but its focus is the action of Lie groups on such manifolds."
Dirac Operators in Riemannian Geometry (Graduate Studies in Mathematics)
Dirac Operators in Riemannian Geometry (Graduate Studies in Mathematics)
"Great brief introduction to differential operators of Dirac type on manifolds. It serves as a good continuation to Nicolaescu's final chapters, as an introduction to spin geometry, as needed to more advanced results like the Atiyah-Index theorem and Seiberg-Witten theory (which even introduces)."
Spin Geometry. (PMS-38)
Spin Geometry. (PMS-38)
The Atiyah-Singer Index Theorem: An Introduction (Lecture Notes in Mathematics)
The Atiyah-Singer Index Theorem: An Introduction (Lecture Notes in Mathematics)
"This is short classic introduces the Atiyah-Singer index theorem and its main corollaries (Hirzebruch, Chern-Gauß-Bonnet...) using characteristic classes and developing a K-theoretic proof. Also dealing with the subsequent fixed point theorems."
Topology and Analysis: The Atiyah-Singer Index Formula and Gauge-Theoretic Physics (Universitext)
Topology and Analysis: The Atiyah-Singer Index Formula and Gauge-Theoretic Physics (Universitext)
Heat Kernels and Dirac Operators (Grundlehren Text Editions)
Heat Kernels and Dirac Operators (Grundlehren Text Editions)
"One of the fundamental classical references on the analytic heat kernel proof of the Atiyah-Index theorem."
Invariance Theory: The Heat Equation and the Atiyah-Singer Index Theorem (Studies in Advanced Mathematics)
Invariance Theory: The Heat Equation and the Atiyah-Singer Index Theorem (Studies in Advanced Mathematics)
"Another of the fundamental classical references on the analytic heat kernel proof of the Atiyah-Index theorem."
Index Theorem. 1 (Translations of Mathematical Monographs)
Index Theorem. 1 (Translations of Mathematical Monographs)
Lectures on Seiberg-Witten Invariants (Lecture Notes in Mathematics)
Lectures on Seiberg-Witten Invariants (Lecture Notes in Mathematics)
The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds (Mathematical Notes, Vol. 44)
The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds (Mathematical Notes, Vol. 44)
Notes on Seiberg-Witten Theory (Graduate Studies in Mathematics, Vol. 28)
Notes on Seiberg-Witten Theory (Graduate Studies in Mathematics, Vol. 28)
"Huge monograph developing the theory of Seiberg-Witten invariants. Very useful for anybody focusing on applications of gauge theory in differential geometry."
Modern Geometric Structures And Fields (Graduate Studies in Mathematics)
Modern Geometric Structures And Fields (Graduate Studies in Mathematics)
Cartan for Beginners: Differential Geometry Via Moving Frames and Exterior Differential Systems (Graduate Studies in Mathematics)
Cartan for Beginners: Differential Geometry Via Moving Frames and Exterior Differential Systems (Graduate Studies in Mathematics)
"A purely differential forms style introduction to differential geometry   la Cartan."
Differential Geometry: Cartan's Generalization of Klein's Erlangen Program (Graduate Texts in Mathematics, Vol. 166)
Differential Geometry: Cartan's Generalization of Klein's Erlangen Program (Graduate Texts in Mathematics, Vol. 166)
"Development of the basic theory with the philosophy of Klein's action of groups."
Analysis and Algebra on Differentiable Manifolds: A Workbook for Students and Teachers
Analysis and Algebra on Differentiable Manifolds: A Workbook for Students and Teachers
"This book is a must have for any student, above all for self-studying. It is a collection of solved problems for any of the standard chapters of a typical book on differential geometry. It contains a detailed appendix full of important formulas and results to use."
Elementary Topics in Differential Geometry (Undergraduate Texts in Mathematics)
Elementary Topics in Differential Geometry (Undergraduate Texts in Mathematics)
An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised, Volume 120, Second Edition (Pure and Applied Mathematics)
An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised, Volume 120, Second Edition (Pure and Applied Mathematics)
Elementary Differential Geometry, Revised 2nd Edition, Second Edition
Elementary Differential Geometry, Revised 2nd Edition, Second Edition