- Home Page /
- Books /
- Textbooks & Study Guides /
- Science & Mathematics /
- Mathematics /
- Geometry /
- Differential Geometry: A Rigorous Introductio...
Item #:
258273627
Differential Geometry: A Rigorous Introduction
Item #:
258273627
ZAR 855
Price Details
Excluding Shipping & Custom charges ( Shipping and custom charges will be calculated on checkout )
*All items will import from EU
0 ratings
Write a review
In stock
Imported from EU store
QTY:
Order now and get it around Friday, October 30
Secured transaction
Ubuy works hard to protect your security and privacy. Our advanced payment security system ensures confidentiality by encrypting your information during transmission using AES (Advanced Encryption Standards) and SSL (Secure Socket Layer) protocols. Your payment details are 100% secure as we do not share your payment details with third party sellers.
Our Top Logistics Partners
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.
Fast
Shipping
Free
Return*
Secure Packaging
100% Original Products
PCI DSS Compliance
ISO 27001 Certified
Product Details
- 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.The sign conventions follow Lee and do Carmo: the sectional curvature of the round unit sphere is +1, and the shape operator of the outward-oriented sphere is minus the identity. Definitions, theorems, propositions, lemmas, corollaries, examples, and remarks share a single numbering stream within each chapter, so Proposition 1.5 and Theorem 1.8 both live in Chapter 1.What is inside14 main chapters and 4 appendices across 170 pages, organized into three parts that read in sequence20 instructional figures with precise captions: the Frenet frame, the osculating circle, the Gauss map, elliptic/parabolic/hyperbolic points, geodesic triangles and angle excess, atlas and transition maps, flow boxes, pullback of forms, the exponential map, Jacobi fields and geodesic spread, and a three-panel comparison of positive, zero, and negative curvature68 exercises graded from routine to substantial, at the end of Chapters 2–5, 8, 12, 13, and at the end of each appendixFull solutions to every main-chapter exercise and to odd-numbered appendix exercises, collected in a dedicated Solutions section at the back of the bookFour self-contained appendices covering point-set topology, multilinear algebra and bilinear forms, ordinary differential equations, and Sard's theorem — provided for reference so the main chapters stay focusedPrerequisitesFluency in linear algebra, real analysis on Rⁿ (continuity, differentiation, the implicit and inverse function theorems), and the basic language of point-set topology. Familiarity with ordinary differential equations is useful; the results actually needed are reviewed in Appendix C. No prior exposure to differential geometry, smooth manifolds, or tensor analysis is assumed.Who this book is forFirst-year graduate students in mathematics beginning a formal course in differential geometry or Riemannian geometryAdvanced undergraduates preparing for graduate study, wanting the classical and modern pictures in one volumePhysicists, engineers, and computer scientists who need a mathematically complete reference for curvature, geodesics, and the manifold apparatusAnyone returning to the subject who wants a compact, theorem-by-theorem treatment with every proof present and every sign convention fixedDifferential Geometry: A Rigorous Introduction is a textbook, not an informal tour. Every theorem is stated precisely, proved in full, and placed in the logical architecture of the subject. The figures are aids to geometric intuition; the proofs do not depend on them.
| Publisher | Independently published |
| Publication date | 22 April 2026 |
| Language | English |
| Print length | 200 pages |
| ISBN-13 | 979-8258292360 |
| Dimensions | 17.78 x 1.17 x 25.4 cm |
Product Description
Differential Geometry: A Rigorous Introduction
Have any Query? Chat with us
Customer Questions & Answers
-
Question:
How to Shop Differential Geometry: A Rigorous Introduction Online From Ubuy?
Answer: It’s easy to shop Differential Geometry: A Rigorous Introduction online from Ubuy. You just have to search for the product, choose your shipping method while checking out and get it delivered to your location. -
Question:
Is Differential Geometry: A Rigorous Introduction Available to Shop Online in South Africa?
Answer: Yes, at Ubuy South Africa this product is available for you to shop at a reasonable price. The Differential Geometry: A Rigorous Introduction is not available locally but you can trust us with our express shipping services. -
Question:
How Long Does It Take to Get Product After Placing the Order?
Answer: The delivery time of your ordered product varies as per what you've ordered and the shipping method that you've chosen. The estimated delivery time is mentioned during the checkout process, so be carefree while shopping.
English edition Aiden Sol Format: Paperback Geometry Editorial Review
No editorial reviews found
Customer Reviews & Ratings
1 customers ratings
-
5 Star
100%
-
4 Star
0%
-
3 Star
0%
-
2 Star
0%
-
1 Star
0%
Review this product
Share your thoughts with other customers
Platform Trust & Buyer Confidence
VJ
Vernon
Verified buyer
“I ordered the Flowtime Biofeedback Headband from Ubuy. I reside in South Africa. I was very impressed with the ease of purchase, parcel tracking, and speed of service. My package arrived much earlier than anticipated. I am very impressed with the service and would highly recommend it. Hence the 5 stars.”
22 July 2026 · via Trustpilot
K
Kobus
Verified buyer
“From the moment I placed my order, I was kept informed about the status of my order. I received my goods in good condition only a few days after placing the order. Well done, thank you.”
17 July 2026 · via Trustpilot
MM
Mlungisi
Verified buyer
“I bought Huckberry Flint & Tinder blazer at Ubuy. My request for a return was rejected at first but later I received an apology message willing to resolve the matter without placing any burden on me. I really appreciate their resolution. The blazer was collected yesterday by DHL couriers on behalf of Ubuy. They can only do a refund and not offer a bigger size as i expected, but i am fine with that too. ”
5 August 2026 · via Trustpilot
LK
Lawrence
Verified buyer
“Excellent service and received my shipment in order. ”
15 September 2026 · via Trustpilot
S
Sonnie
Verified buyer
“What a life saver ! I live in South Africa and can't find Dr Elseys Clean Protein Cat Food locally. Ubuy helped me to import this food and my diabetic cat is now in remission !!”
18 September 2026 · via Trustpilot
WHY SHOP WITH US
Secure Checkout
Global Delivery
Easy Returns
Genuine Products
Product Price History
Important information
- Limitations : For products shipped internationally, please note that any manufacturer warranty may not be valid; manufacturer service options may not be available; product manuals, instructions, and safety warnings may not be in destination country languages; the products (and accompanying materials) may not be designed in accordance with destination country standards, specifications, and labeling requirements; and the products may not conform to destination country voltage and other electrical standards (requiring use of an adapter or converter if appropriate). The recipient is responsible for assuring that the product can be lawfully imported to the destination country. When ordering from Ubuy or its affiliates, the recipient is the importer of record and must comply with all laws and regulations of the destination country.
- Not all the products listed on Ubuy are for sale, as Ubuy is a global search engine. Products are subject to export/trade regulations.
ZAR 855
Order now and get it around Friday, October 30
This item is not restrict in my country.(Please click on above link if this item is not restrict in your country, So our team will review and allow.)
QTY:
Secured transaction
PCI DSS compliant and ISO 27001:2022 certified, with encrypted payments and full buyer protection on every order.
Our Top Logistics Partners
Fastest cross-border delivery
Features & Benefits
- Graduate-level textbook covering classical and modern differential geometry.
- Includes full proofs and develops both curves and surfaces in R³ and smooth manifolds.
- Structured into 14 chapters and 4 appendices, totaling 170 pages.
- Features 20 instructional figures and 68 graded exercises with detailed solutions.
- Self-contained appendices ensure main chapters remain focused on core concepts.
- No prior exposure to differential geometry required; suitable for those with a solid foundation in linear algebra and real analysis.
Ubuy Assurance
Experience worry-free shopping with 100% original products, PCI DSS-compliant payment security, ISO 27001-certified data protection, the fastest cross-border delivery, free returns *, and secure packaging on every order.