[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14403/jcms.2011.24.4.18

CURVATURE TENSOR FIELDS ON HOMOGENEOUS SPACES

Park, Joon-Sik (Department of Mathematics Busan University of Foreign Studies)

Publication Information

Journal of the Chungcheong Mathematical Society / v.24, no.4, 2011 , pp. 825-832 More about this Journal

Abstract

In this paper, we make a minute and detailed proof of a part which is omitted in the process of obtaining the value of the curvature tensor for an invariant affine connection at the point {H} of a reductive homogeneous space G/H in the paper 'Invariant affine connections on homogeneous spaces' by K. Nomizu.

Keywords

reductive homogeneous space; invariant connection; curvature tensor field;

Citations & Related Records

Reference

1	S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, New York, 1978.
2	S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, John Wiley and Sons, New York, Vol. 1, 1963; Vol. 2, 1969.
3	K. Nomizu, Invariant affine connections on homogeneous spaces, Amer. J. Math. 76 (1954), 33-65. DOI ScienceOn
4	J.-S. Park, Projectively flat Yang-Mills connections, Kyushu J. Math. 64 (2010), no. 1, 49-58.
5	J.-S. Park, Invariant Yang-Mills connections with Weyl structure, J. Geometry and Physics 60 (2010), 1950-1957. DOI ScienceOn
6	W. A. Poor, Differential Geometric Structures, McGraw-Hill. Inc., 1981.
7	F. Tricerri and L. Vanhecke, Homogeneous Structures on Riemannian Manifolds, Cambridge University Press, 1983.