Acknowledgement
Supported by : Pukyong National University
References
- B. Alexandrov, S. Ivanov, Weyl structure with positive Ricci tensor, Differential Geom. Appl. 18 (2003), no. 3, 343-350. https://doi.org/10.1016/S0926-2245(03)00010-X
- F. Dillen, K. Nomizu and L. Vranken, Conjugate connections and Radon's theorem in affine differential geometry, Monatsh Math. 109 (1990), no. 3, 221- 235. https://doi.org/10.1007/BF01297762
- S. Dragomir, T. Ichiyama and H. Urakawa, Yang-Mills theory and conjugate connections, Differential Geom. Appl. 18 (2003), no. 2, 229-238. https://doi.org/10.1016/S0926-2245(02)00149-3
- M. A. Guest, Geometry of maps between generalized flag manifolds, J. Differential Geom. 25 (1987), 223-247. https://doi.org/10.4310/jdg/1214440851
- S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces, Academic Press, New York, 1978.
- M. Itoh, Compact Einstein-Weyl manifolds and the associated constant, Osaka J. Math. 35 (1998), no. 3, 567-578.
- S. Kobayashi, Differential Geometry of Connections and Gauge Theory, Shokabo (in Japanese), Tokyo, 1990.
- A. B. Madsen, H. Pedersen, Y.S. Poon and A. Swann, Compact Einstein-Weyl manifolds with large symmetry group, Duke Math. J. 88 (1997), no. 3, 407-434. https://doi.org/10.1215/S0012-7094-97-08817-7
- K. Nomizu and T. Sasaki, Affine Differential Geometry-Geometry of Affine Immersions, Cambridge, 1994.
- J.-S. Park, Yang-Mills connections on the orthonormal frame bundles over Einstein normal homogeneous manifolds, Int. J. of Pure & Appli. Math. 5 (2003), 213-223.
- J.-S. Park, Critical homogeneous metrics on the Heisenberg manifold, Int. In- form. Sci. 11 (2005), 31-34.
- J.-S. Park, The conjugate connection of a Yang-Mills connection, Kyushu J. Math. 62 (2008), no. 1, 217-220. https://doi.org/10.2206/kyushujm.62.217
- J.-S. Park, Yang-Mills connections with Weyl structure, Proc. Japan Acad. 84 (2008), no. 7, 129-132. https://doi.org/10.3792/pjaa.84.129
- J.-S. Park, Projectively flat Yang-Mills connections, Kyushu J. Math. 64 (2010), no. 1, 49-58.
- J.-S. Park, Invariant Yang-Mills connections with Weyl structure, J. Geometry and Physics 60 (2010), 1950-1957. https://doi.org/10.1016/j.geomphys.2010.08.003
- H. Pedersen, Y.S. Poon and A. Swann, The Hitchin-Thorpe inequality for Einstein-Weyl manifolds, Bull. London Math. Soc. 26 (1994), 191-194. https://doi.org/10.1112/blms/26.2.191
- H. Pedersen, Y.S. Poon and A. Swann, Einstein-Weyl deformations and submanifolds, Internat. J. Math. 7 (1996), 705-719. https://doi.org/10.1142/S0129167X96000372
- H. Pedersen and A. Swann, Riemannian submersions, four-manifolds, and Einstein-Weyl geometry, Proc. London Math. Soc. 66 (1993), 381-399. https://doi.org/10.1112/plms/s3-66.2.381
- H. Pedersen and A. Swann, Einstein-Weyl geometry, the Bach tensor and conformal scalar curvature, J. reine angew. Math. 441 (1993), 99-113.
- H. Pedersen and K.P. Tod, Three dimensional Einstein geometry, Adv. Math. 97 (1993), 74-109. https://doi.org/10.1006/aima.1993.1002
- K. P. Tod, Compact 3-dimensional Einstein-Weyl structures, J. London Math. Soc. 45 (1992), 341-351. https://doi.org/10.1112/jlms/s2-45.2.341
- H. Urakawa, Yang-Mills theory in Einstein-Weyl geometry and affne differen- tial geometry, Rev. Bull. Calcutta Math. Soc. 10 (2002), 7-18.