The DOI matches its Crossref record.
Geometry of Manifolds
Abstract
First published in 1964, this book served as a text on differential geometry to several generations of graduate students all over the world. The first half of the book (Chapters 1-6) presents basics of the theory of manifolds, vector bundles, differential forms, and Lie groups, with a special emphasis on the theory of linear and affine connections. The second half of the book (Chapters 7-11) is devoted to Riemannian geometry. Following the definition and main properties of Riemannian manifolds, the authors discuss the theory of geodesics, complete Riemannian manifolds, and curvature. Next, the
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cited by
Burago, D., Burago, Y., & Ivanov, S. (2001) · Graduate Studies in Mathematics · doi:10.1090/gsm/033 · Cited by 2,598
Riemannian center of mass and mollifier smoothing
Karcher, H. (1977) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.3160300502 · Cited by 995
Grove, K., & Shiohama, K. (1977) · The Annals of Mathematics · doi:10.2307/1971164 · Cited by 286
Chern, S. S. (1966) · Bulletin of the American Mathematical Society · doi:10.1090/s0002-9904-1966-11473-8 · Cited by 159
Geometry of the transport equation in multicomponent WKB approximations
Emmrich, C., & Weinstein, A. (1996) · Communications in Mathematical Physics · doi:10.1007/bf02099256 · Cited by 89
Metadata
- Authors
- Bishop, R., & Crittenden, R.
- Venue
- American Mathematical Society eBooks
- Publisher
- American Mathematical Society
- Published
- 2001-08-28
- OpenAlex
- W1595217145
- Cited by
- 780
- References
- 0
- FWCI
- 17.21
- Type
- book
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Geometry of Manifolds. https://app.cochat.ai/papers/10.1090/chel/344
- The paper
- Bishop, R., & Crittenden, R. (2001). Geometry of Manifolds. American Mathematical Society eBooks. https://doi.org/10.1090/chel/344
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
