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초록· 키워드
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Let G be a compact and connected semisimple Lie group, H a closed subgroup, g (resp. h) the Lie algebra of G (resp. H), B the Killing form of g, g the normal metric on the homogeneous space G/H which is induced by -B. Let D be an invarint connection with Weyl structure (D, g, ${\omega}$) in the tangent bundle over the normal homogeneous Riemannian manifold (G/H, g) which is projectively flat. Then, the affine connection D on (G/H, g) is a Yang-Mills connection if and only if D is the Levi-Civita connection on (G/H, g).
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참고문헌 (18)
참고문헌 신청
J.E. D'Atri / 1979 / Naturally reductive metrics and Einstein metrics on compact Lie groups / Memoirs of Amer. Math. Soc 18(215):1~72
S. Dragomir / 2003 / Yang-Mills theory and conjugate connections / Dierential Geom. Appl 18(2):229~238
S. Helgason / 1978 / Dierential Geometry, Lie Groups and Symmetric Spaces / Academic Press
M. Itoh / 1998 / Compact Einstein-Weyl manifolds and the associated constant / Osaka J. Math 35(3):567~578
S. Kobayashi / 1963 / Foundation of Dierential Geometry, Vol.I / Wiley- Interscience
S. Dragomir / 2003 / Yang-Mills theory and conjugate connections / Dierential Geom. Appl 18(2):229~238
S. Helgason / 1978 / Dierential Geometry, Lie Groups and Symmetric Spaces / Academic Press
M. Itoh / 1998 / Compact Einstein-Weyl manifolds and the associated constant / Osaka J. Math 35(3):567~578
S. Kobayashi / 1963 / Foundation of Dierential Geometry, Vol.I / Wiley- Interscience
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