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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeApr 12th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[John M. Lee]], _Riemannian manifolds. An introduction to curvature_. Graduate Texts in Mathematics 176 (1997), Springer. ISBN: 0-387-98271-X. Second Edition (retitled): *Introduction to Riemannian Manifolds* (2018), Springer. ISBN: 978-3-319-91754-2 ([doi:10.1007/978-3-319-91755-9](https://doi.org/10.1007/978-3-319-91755-9)) <a href="https://ncatlab.org/nlab/revision/diff/Riemannian+geometry/16">diff</a>, <a href="https://ncatlab.org/nlab/revision/Riemannian+geometry/16">v16</a>, <a href="https://ncatlab.org/nlab/show/Riemannian+geometry">current</a>

   added pointer to:

   • John M. Lee, Riemannian manifolds. An introduction to curvature. Graduate Texts in Mathematics 176 (1997), Springer. ISBN: 0-387-98271-X. Second Edition (retitled): Introduction to Riemannian Manifolds (2018), Springer. ISBN: 978-3-319-91754-2 (doi:10.1007/978-3-319-91755-9)

   diff, v16, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeDec 5th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Jürgen Jost]], *Riemannian Geometry and Geometric Analysis*, Springer (2017) &lbrack;[doi:10.1007/978-3-319-61860-9](https://doi.org/10.1007/978-3-319-61860-9)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/Riemannian+geometry/19">diff</a>, <a href="https://ncatlab.org/nlab/revision/Riemannian+geometry/19">v19</a>, <a href="https://ncatlab.org/nlab/show/Riemannian+geometry">current</a>

   added pointer to:

   • Jürgen Jost, Riemannian Geometry and Geometric Analysis, Springer (2017) [doi:10.1007/978-3-319-61860-9]

   diff, v19, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJan 19th 2024
   • (edited Jan 19th 2024)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Bernhard Riemann]], *[[Über die Hypothesen, welche der Geometrie zu Grunde liegen]]*, Göttingen (1845) &lbrack;[doi:10.1007/978-3-642-35121-1](https://doi.org/10.1007/978-3-642-35121-1)&rbrack; Engl. transl: [[William Clifford]]: *[[On the hypotheses which underlie geometry]]*, Nature **VIII** (1873) 183-184 &lbrack;[doi:10.1007/978-3-319-26042-6](https://doi.org/10.1007/978-3-319-26042-6)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/Riemannian+geometry/20">diff</a>, <a href="https://ncatlab.org/nlab/revision/Riemannian+geometry/20">v20</a>, <a href="https://ncatlab.org/nlab/show/Riemannian+geometry">current</a>

   added pointer to:

   • Bernhard Riemann, Über die Hypothesen, welche der Geometrie zu Grunde liegen, Göttingen (1845) [doi:10.1007/978-3-642-35121-1]

     Engl. transl: William Clifford: On the hypotheses which underlie geometry, Nature VIII (1873) 183-184 [doi:10.1007/978-3-319-26042-6]

   diff, v20, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeMay 16th 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[William M. Boothby]], *An introduction to differentiable manifolds and Riemannian geometry*, Academic Press (1986), Elsevier (2002) &lbrack;[pdf](https://aetemad.iut.ac.ir/sites/aetemad.iut.ac.ir/files/files_course/william_m._boothby_an_introduction_to_differentibookfi.org_.pdf), [ISBN:9780121160517](https://shop.elsevier.com/books/an-introduction-to-differentiable-manifolds-and-riemannian-geometry-revised/boothby/978-0-08-057475-2)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/Riemannian+geometry/23">diff</a>, <a href="https://ncatlab.org/nlab/revision/Riemannian+geometry/23">v23</a>, <a href="https://ncatlab.org/nlab/show/Riemannian+geometry">current</a>

   added pointer to:

   • William M. Boothby, An introduction to differentiable manifolds and Riemannian geometry, Academic Press (1986), Elsevier (2002) [pdf, ISBN:9780121160517]

   diff, v23, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeMay 18th 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointers to: * [[Élie Cartan]] (translated by Vladislav Goldberg from Cartan's lectures at the Sorbonne in 1926–27): *Riemannian Geometry in an Orthogonal Frame*, World Scientific (2001) &lbrack;[doi:10.1142/4808](https://doi.org/10.1142/4808), [pdf](https://softbank.iust.ac.ir/MathBooks/c/Cartan%20-%20Riemannian%20Geometry%20in%20an%20Orthogonal%20Frame.pdf)&rbrack; * [[Élie Cartan]] (translated by Robert Hermann from Cartan's lectures in 1951): *Geometry of Riemannian Spaces*, Lie Groups: History, Frontiers and Applications **XIII**, Math Sci Press (1983) &lbrack;[ark:/13960/s28rzmj9xrv](https://archive.org/details/geometryofrieman0013cart)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/Riemannian+geometry/24">diff</a>, <a href="https://ncatlab.org/nlab/revision/Riemannian+geometry/24">v24</a>, <a href="https://ncatlab.org/nlab/show/Riemannian+geometry">current</a>

   added pointers to:

   • Élie Cartan (translated by Vladislav Goldberg from Cartan’s lectures at the Sorbonne in 1926–27): Riemannian Geometry in an Orthogonal Frame, World Scientific (2001) [doi:10.1142/4808, pdf]

   • Élie Cartan (translated by Robert Hermann from Cartan’s lectures in 1951): Geometry of Riemannian Spaces, Lie Groups: History, Frontiers and Applications XIII, Math Sci Press (1983) [ark:/13960/s28rzmj9xrv]

   diff, v24, current

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeJun 6th 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded the following pointers (here and in related entries): * [[Barrett O'Neill]], *Semi-Riemannian Geometry With Applications to Relativity*, Pure and Applied Mathematics **103**, Academic Press (1983) &lbrack;[ISBN:9780125267403](https://shop.elsevier.com/books/semi-riemannian-geometry-with-applications-to-relativity/oneill/978-0-12-526740-3)&rbrack; * [[Shlomo Sternberg]], *Semi-Riemannian Geometry and General Relativity* (2003) &lbrack;[pdf](https://people.math.harvard.edu/~shlomo/docs/semi_riemannian_geometry.pdf), [ark:/13960/t5m927d2v](https://archive.org/details/Shlomo_Sternberg__SemiRiemann_Geometry_and_General_Relativity/)&rbrack; * [[Shlomo Sternberg]], *Curvature in Mathematical Physics*, Dover (2012) &lbrack;[ISBN:9780486478555](https://store.doverpublications.com/products/9780486478555)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/Riemannian+geometry/28">diff</a>, <a href="https://ncatlab.org/nlab/revision/Riemannian+geometry/28">v28</a>, <a href="https://ncatlab.org/nlab/show/Riemannian+geometry">current</a>

   added the following pointers (here and in related entries):

   • Barrett O’Neill, Semi-Riemannian Geometry With Applications to Relativity, Pure and Applied Mathematics 103, Academic Press (1983) [ISBN:9780125267403]

   • Shlomo Sternberg, Semi-Riemannian Geometry and General Relativity (2003) [pdf, ark:/13960/t5m927d2v]

   • Shlomo Sternberg, Curvature in Mathematical Physics, Dover (2012) [ISBN:9780486478555]

   diff, v28, current

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeJun 21st 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Luther P. Eisenhart]], *Riemannian Geometry*, Princeton University Press (1925, 1950) &lbrack;[ISBN:9780691023533](https://press.princeton.edu/books/paperback/9780691023533/riemannian-geometry), [ark:/13960/t47q47r0k](https://archive.org/details/in.ernet.dli.2015.524829), [pdf](http://www.uop.edu.pk/ocontents/Eisenhart-RiemannianGeometry.pdf)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/Riemannian+geometry/29">diff</a>, <a href="https://ncatlab.org/nlab/revision/Riemannian+geometry/29">v29</a>, <a href="https://ncatlab.org/nlab/show/Riemannian+geometry">current</a>

   added pointer to:

   • Luther P. Eisenhart, Riemannian Geometry, Princeton University Press (1925, 1950) [ISBN:9780691023533, ark:/13960/t47q47r0k, pdf]

   diff, v29, current

8. • CommentRowNumber8.
   • CommentAuthorUrs
   • CommentTimeJun 21st 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Thomas J. Willmore]], *Riemannian Geometry*, Oxford University Press (1996) &lbrack;[ISBN:9780198514923](https://global.oup.com/academic/product/riemannian-geometry-9780198514923?cc=de&lang=en&), [ark:/13960/t4jn0093w](https://archive.org/details/riemanniangeomet0000will)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/Riemannian+geometry/30">diff</a>, <a href="https://ncatlab.org/nlab/revision/Riemannian+geometry/30">v30</a>, <a href="https://ncatlab.org/nlab/show/Riemannian+geometry">current</a>

   added pointer to:

   • Thomas J. Willmore, Riemannian Geometry, Oxford University Press (1996) [ISBN:9780198514923, ark:/13960/t4jn0093w]

   diff, v30, current