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authorEric Gourgoulhon <eric.gourgoulhon@obspm.fr>2015-06-25 17:26:03 +0200
committerEric Gourgoulhon <eric.gourgoulhon@obspm.fr>2015-06-25 17:26:03 +0200
commitf4c9f0f37fa3e3ad9b774b6099b3bbbbc40b5a28 (patch)
treefbfaba3e48ce88e62b2e3c76c8aac1dc1ccae7ad
parentCorrect doctests on differentiable manifolds (diff)
Start to improve the documentation of differentiable manifolds
-rw-r--r--src/doc/en/reference/manifolds/diff_manifold.rst18
-rw-r--r--src/doc/en/reference/manifolds/index.rst2
-rw-r--r--src/sage/manifolds/differentiable/manifold.py17
3 files changed, 34 insertions, 3 deletions
diff --git a/src/doc/en/reference/manifolds/diff_manifold.rst b/src/doc/en/reference/manifolds/diff_manifold.rst
new file mode 100644
index 0000000..1dc6059
--- /dev/null
+++ b/src/doc/en/reference/manifolds/diff_manifold.rst
@@ -0,0 +1,18 @@
+Differentiable manifolds
+========================
+
+.. toctree::
+ :maxdepth: 2
+
+ sage/manifolds/differentiable/manifold
+
+ sage/manifolds/differentiable/chart
+
+ sage/manifolds/differentiable/scalarfield_algebra
+
+ sage/manifolds/differentiable/scalarfield
+
+ sage/manifolds/differentiable/manifold_homset
+
+ sage/manifolds/differentiable/diff_map
+
diff --git a/src/doc/en/reference/manifolds/index.rst b/src/doc/en/reference/manifolds/index.rst
index 5d0cb0e..56f9e1f 100644
--- a/src/doc/en/reference/manifolds/index.rst
+++ b/src/doc/en/reference/manifolds/index.rst
@@ -15,6 +15,8 @@ More documentation (in particular example worksheets) can be found
manifold
+ diff_manifold
+
sage/manifolds/utilities
.. include:: ../footer.txt
diff --git a/src/sage/manifolds/differentiable/manifold.py b/src/sage/manifolds/differentiable/manifold.py
index 1e6347e..cb5e517 100644
--- a/src/sage/manifolds/differentiable/manifold.py
+++ b/src/sage/manifolds/differentiable/manifold.py
@@ -1,7 +1,8 @@
r"""
Differentiable manifolds
-Given a topological field `K` (in most applications, `K = \RR` or `K = \CC`),
+Given a topological field `K` (in most applications, `K = \RR` or `K = \CC`;
+see Ser92_ for `K = \QQ_p` and Bertram for more general fields),
a *differentiable manifold over* `K` is a topological manifold `M` over `K`
equipped with an atlas whose transitions maps are of class `C^k` (i.e.
`k`-times continuously differentiable) for a fixed positive integer `k`
@@ -255,11 +256,21 @@ AUTHORS:
REFERENCES:
+.. _Ser92:
+
+- J.-P. Serre : *Lie Algebras and Lie Groups*, 2nd ed., Springer
+ (Berlin) (1992); :doi:`10.1007/978-3-540-70634-2`
+
+
- J.M. Lee : *Introduction to Smooth Manifolds*, 2nd ed., Springer (New York)
- (2013)
+ (2012); :doi:`10.1007/978-1-4419-9982-5`
- S. Kobayashi & K. Nomizu : *Foundations of Differential Geometry*, vol. 1,
Interscience Publishers (New York) (1963)
-- D. Huybrechts : *Complex Geometry*, Springer (Berlin) (2005)
+- D. Huybrechts : *Complex Geometry*, Springer (Berlin) (2005);
+ :doi:`10.1007/b137952`
+- W. Bertram : *Differential Geometry, Lie Groups and Symmetric Spaces over
+ General Base Fields and Rings*, Memoirs of the American Mathematical
+ Society, vol. 192 (2008); :doi:`10.1090/memo/0900`; :arxiv:`math/0502168`
"""