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2014

Riemannian Geometry: Definitions, Pictures, and Results

Marsh, Adam

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A pedagogical but concise overview of Riemannian geometry is provided, in the context of usage in physics.

The emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions, alternative notations and jargon, and relevant facts and theorems.
Special attention is given to detailed figures and geometric viewpoints, some of which would seem to be novel to the literature.
Topics are avoided which are well covered in textbooks, such as historical motivations, proofs and derivations, and tools for practical calculations.

Riemannian Geometry: Definitions, Pictures, and Results · Around

Built on

S. Kobayashi and K. Nomizu, Foundations of Differential Geometry
1963
Earlier work this paper cites.
C. Misner, K. Thorne and J. Wheeler, Gravitation
1973
Earlier work this paper cites.
A. Gray, “The volume of a small geodesic ball of a Riemannian manifold,” The Michigan Mathematical Journal 20 (1974), no. 4, 329-344, http://projecteuclid.org/euclid.mmj/1029001150
1974
Earlier work this paper cites.

Similar

T. Frankel, Gravitational Curvature
1979
Cited alongside, same era.
R. Wald, General Relativity
Original
1984
Cited alongside, same era.
M. Göckeler and T. Schücker, Differential Geometry, Gauge Theories, and Gravity
1987
Cited alongside, same era.

Then

M. do Carmo, Riemannian Geometry
1992
Later among the works it cites.
T. Frankel, The Geometry of Physics
1997
Later among the works it cites.
P. Petersen, Riemannian Geometry
2006
Later among the works it cites.

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