Non-Riemannian Geometry
Abstract
The use of the differential geometry of a Riemannian space in the mathematical formulation of physical theories led to important developments in the geometry of such spaces. The concept of parallelism of vectors, as introduced by Levi-Civita, gave rise to a theory of the affine properties of a Riemannian space. Covariant differentiation, as developed by Christoffel and Ricci, is a fundamental process in this theory. Various writers, notably Eddington, Einstein and Weyl, in their efforts to formulate a combined theory of gravitation and electromagnetism, proposed a simultaneous generalization o
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Without further phenomena, a Kantowski-Sachs universe would be singular and oscillatory, and would not exceed the size of the parent black hole.
“Without further phenomena, such a universe would be singular and oscillatory [32], and would not exceed the size of the parent black hole.”
From A nonsingular, anisotropic universe in a black hole with torsion and particle production (2021) · cites this paper as [32]
Cited by
Sorted by citations
A nonsingular, anisotropic universe in a black hole with torsion and particle production
Popławski, N. J. (2021) · General Relativity and Gravitation · doi:10.1007/s10714-021-02790-7 · Cited by 12 · see citing works
- Authors
- Eisenhart, L.
- Corresponding author
- Eisenhart, L.
- Venue
- Colloquium Publications
- Publisher
- American Mathematical Society
- Published
- 1927-12-31
- ISSN
- 0065-9258 (ISSN-L)
- OpenAlex
- W1565219082
- Cited by
- 512
- References
- 0
- Citations by year
- 2026: 4 · 2025: 9 · 2024: 11 · 2023: 16 · 2022: 17 · 2021: 24 · 2020: 19 · 2019: 17 · 2018: 17 · 2017: 9 · 2016: 11 · 2015: 9 · 2014: 4 · 2013: 12 · 2012: 9
- FWCI
- 24.75
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Colloquium Publications - American Mathematical Society/Colloquium Publications (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Advanced Differential Geometry Research
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Mathematics › Applied Mathematics › Geometric Analysis and Curvature Flows
- Keywords
- non-Riemannian geometry, Riemannian geometry, affine geometry, covariant derivative, Levi-Civita connection, general relativity, unified field theory, Weyl geometry
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
