Open Daily: 10am - 10pm | Alley door pickup 10am - 7pm 3038 Hennepin Ave Minneapolis, MN
612-822-4611

  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Differential Geometry: A Rigorous Introduction

Differential Geometry: A Rigorous Introduction

Sol, Aiden

Paperback

General MathematicsGeometry

ISBN13: 9798258292360
Publisher: Independently Published
Published: Apr 22 2026
Pages: 202
Weight: 0.79
Height: 0.43 Width: 7.00 Depth: 10.00
Language: English
A concise and rigorous introduction to differential geometry, taking the reader from curves in three-space to the comparison theorems of Riemannian geometry in a single self-contained volume.

Differential Geometry: A Rigorous Introduction is a graduate-level textbook that treats both the classical and modern phases of the subject, in that order, with full proofs. Part I develops the geometry of curves and surfaces in R3: parametrization, curvature and torsion, the Frenet-Serret formulas, regular surfaces, the first and second fundamental forms, the Gauss map, and Gaussian curvature, culminating in the Theorema Egregium and the local and global Gauss-Bonnet theorems. Part II recasts these ideas in coordinate-free language: smooth manifolds, the tangent bundle, vector fields and flows, the rank theorem and Whitney embedding, the cotangent bundle and differential forms, and Stokes' theorem on oriented manifolds with boundary. Part III develops Riemannian geometry proper: metrics and the Levi-Civita connection, geodesics and the exponential map, the Hopf-Rinow theorem, the Riemann curvature tensor and sectional curvature, Jacobi fields, and the comparison theorems of Bonnet-Myers and Cartan-Hadamard.

Also from

Sol, Aiden

View All

Also in

Geometry

View All