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Results tagged with riemannian-geometry
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user 32389
Riemannian Geometry is a subfield of Differential Geometry, which specifically studies "Riemannian Manifolds", manifolds with "Riemannian Metrics", which means that they are equipped with continuous inner products.
5
votes
Riemann's formula for the metric in a normal neighborhood
Still another approach to the Riemann normal coordinates expansion formula can be found in http://arxiv.org/abs/gr-qc/9712092 (A Closed Formula for the Riemann Normal Coordinate Expansion, by U. Muell …
- 16.5k
2
votes
Accepted
References on the Free Loop Space
This survey paper on the Morse theory and closed geodesics: http://arxiv.org/abs/1406.3107 (Morse theory, closed geodesics, and the homology of free loop spaces, by Alexandru Oancea) provides a lot of …
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3
votes
Weyl tube formula for manifolds with boundary
I think Alfred Gray's book "Tubes" https://www.springer.com/gp/book/9783764369071 is relevant. See also https://www.sciencedirect.com/science/article/pii/0040938382900052 (Comparison theorems for the …
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6
votes
0
answers
265
views
Gravity, connection, and curvature
Starting with Synge and Fock, many modern authors identify gravity with curvature. On the other hand, Einstein always emphasized that gravity should be equated with a connection, but not with curvatur …
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6
votes
Yang-Mills equations are not elliptic
In fact Yang-Mills equations are elliptic modulo gauge transformations. In simple terms this can be explained as follows (credit: Jonathan Evans, http://www.homepages.ucl.ac.uk/~ucahjde/yangmills.htm) …
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14
votes
If a triangle can be displaced without distortion, must the surface have constant curvature?
Already Riemann in his famous "On the Hypotheses Which Lie at the Bases of Geometry" concludes that the spaces of constant curvature are precisely those in which figures can move without distortion. H …
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4
votes
Alternative proof of Varadhan's formula on Riemann manifolds
Varadhan's result was extended to wider class of operators and manifolds by Molchanov: http://iopscience.iop.org/0036-0279/30/1/R01 (Diffusion processes and Riemannian geometry). See also http://arxiv …
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12
votes
General Relativity and Differential Geometry intuitions of Second Bianchi Identity
From The "Foreword to Feynman Lectures on Gravitation" by John Preskill and Kip S. Thorne:
In §9.3, Feynman comments that he knows no geometrical interpretation of
the Bianchi identity, and he s …
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