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P. A. Shirokov’s work on the geometry of symmetric spaces. (English. Russian original) Zbl 0911.53031

J. Math. Sci., New York 89, No. 3, 1253-1260 (1998); translation from Itogi Nauki Tekh., Ser. Sovrem Mat. Prilozh., Temat. Obz. 30, 125-137 (1996).
This is a short commemorative paper about the work by P. A. Shirokov written by his son. The author reminds the year 1937 when Élie Cartan became a laureate of the Lobachevskii prize in Kazan under the patronage of Shirokov. Later, P. A. Shirokov translated a number of Cartan’s works.
P. A. Shirokov started his scientific work on symmetric spaces independently in 1925. He classified all conformally Euclidean symmetric spaces and studied also those with indefinite metrics. He introduced the concept of a Kähler symmetric space in 1925 under a different name, and later he found some important classes of these spaces in an original way. Finally, one should mention Shirokov’s work on symmetric projectively flat spaces with affine connection.
The article describes the methods which P. A. Shirokov used in his investigations and some of his results in detail.

MSC:

53C35 Differential geometry of symmetric spaces
01A60 History of mathematics in the 20th century
53C55 Global differential geometry of Hermitian and Kählerian manifolds
53A30 Conformal differential geometry (MSC2010)

Biographic References:

Shirokov, P. A.
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