Shiing-Shen Chern: Quotes about studying

Shiing-Shen Chern was mathematician (1911–2004), born in China and later acquiring U.S. citizenship; made fundamental contributions to differential geometry and topology. Explore interesting quotes on study.

Shiing-Shen Chern: 12 quotes 6 likes

“Integral geometry, started by the English geometer M. W. Crofton, has received recently important developments through the works of W. Blaschke, L. A. Santaló, and others. Generally speaking, its principal aim is to study the relations between the measures which can be attached to a given variety.”

Shiing-Shen Chern

[Differential geometry and integral geometry, Proc. Int. Congr. Math. Edinburgh, 1958, 411–449, http://www.mathunion.org/ICM/ICM1958/Main/icm1958.0441.0453.ocr.pdf]

Study

“The main object of study in differential geometry is, at least for the moment, the differential manifolds, structures on the manifolds (Riemannian, complex, or other), and their admissible mappings. On a manifold the coordinates are valid only locally and do not have a geometric meaning themselves.”

Shiing-Shen Chern

[Differential geometry, its past and its future, Actes, Congrès inter. math, 1970, 41–53, http://www.math.harvard.edu/~hirolee/pdfs/2014-fall-230a-icm1970-chern-differential-geometry.pdf]

Study

“It is well known that in three-dimensional elliptic or spherical geometry the so-called Clifford's parallelism or parataxy has many interesting properties. A group-theoretical reason for the most important of these properties is the fact that the universal covering group of the proper orthogonal group in four variables is the direct product of the universal covering groups of two proper orthogonal groups in three variables. This last-mentioned property has no analogue for orthogonal groups in n (>4) variables. On the other hand, a knowledge of three-dimensional elliptic or spherical geometry is useful for the study of orientable Riemannian manifols of four dimensions, because their tangent spaces possess a geometry of this kind.”

Shiing-Shen Chern

[On Riemannian manifolds of four dimensions, Bulletin of the American Mathematical Society, 51, 12, 1945, 964–971, http://www.ams.org/journals/bull/1945-51-12/S0002-9904-1945-08483-3/S0002-9904-1945-08483-3.pdf]

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