The affine connection in the normal coordinates

被引：0

作者：

Gavrilov A.V. ^{[1
]}

机构：

[1] Siberian Independent Institute, Novosibirsk

来源：

Siberian Advances in Mathematics | 2013年 / 23卷 / 1期

基金：

俄罗斯基础研究基金会;

关键词：

affine connection; composition of exponential maps; normal coordinates;

D O I：

10.3103/S105513441301001X

中图分类号：

学科分类号：

摘要：

We propose a method to calculate the derivatives of the Christoffel symbols in the normal coordinates on a smooth manifold with symmetric affine connection. As an application, we construct an algorithm for computing the Taylor series of the double exponential map. © 2013 Allerton Press, Inc.

引用

页码：1 / 19

页数：18

共 8 条

[1]

Gavrilov A.V., Algebraic properties of covariant derivative and composition of exponential maps, Mat. Tr., 9, 1, pp. 3-20, (2006)

[2]

Gavrilov A.V., The double exponential map and covariant derivation, Sibirsk. Mat. Zh., 48, 1, pp. 68-74, (2007)

[3]

Gavrilov A.V., Higher covariant derivatives, Sibirsk. Mat. Zh., 49, 6, pp. 1250-1262, (2008)

[4]

Gavrilov A.V., Commutation relations on the covariant derivative, J. Algebra, 323, 2, pp. 517-521, (2010)

[5]

Gavrilov A.V., The Leibniz formula for the covariant derivative and some of its applications, Mat. Tr., 13, 1, pp. 63-84, (2010)

[6]

Kobayashi S., Nomizu K., Foundations of Differential Geometry. Vol. II, (1969)

[7]

Sharafutdinov V.A., Geometric symbol calculus for pseudodifferential operators. I

[8]

II, Mat. Tr., 7, 2, pp. 159-206, (2004)

← 1 →