Abstract
Let M be a compact m-dimensional complex manifold and F(M) the holomorphic frame bundle over M. Then π:F(M)→M is a holomorphic principal GL(m;c)-bundle over M. Let G be a complex Lie subgroup of GL(m;c). A holomorphic principal G-subbundle tt:P + M of Fin) is called a holomorphic G-structure on M.
Partially supported by NSF Grant 79-02552.
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References
M. Inoue, S. Kobayashi and T. Ochiai, “Holomorphic affine connections on compact complex surfaces,” J. Fac. Sci. Univ. Tokyo 27 (1980), 247–264.
S. Kobayashi, “First Chern class and holomorphic tensor fields,” Nagoya Math. J. 77 (1980), 5–11.
S. Kobayashi and T. Nagano, “On filtered Lie algebras and geometric structures,” I. J. Math. Mech. 13 (1964), 873–908
S. Kobayashi and T. Nagano, “On filtered Lie algebras and geometric structures,” I. J. Math. Mech. 11. 14 (1965), 513–522
S. Kobayashi and T. Nagano, “On filtered Lie algebras and geometric structures,” I. J. Math. Mech. III. 14 (1965), 679–706.
S. Kobayashi and T. Ochiai, “Holomorphic projective structures on compact complex surfaces,” Math. Ann. 249 (1980), 75–94.
S. Kobayashi and T. Ochiai, “Holomorphic structures modeled after hyperquadrics,” to appear.
T. Ochiai, “Geometry associated with semi-simple flat homogeneous spaces,” Trans. Amer. Math. Soc. 152 (1970), 159–193.
N. Tanaka, “On the equivalence problems associated with a certain class of homogeneous spaces,” J. Math. Sco. Japan 17 (1965), 103–139.
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© 1981 Springer Science+Business Media New York
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Kobayashi, S., Ochiai, T. (1981). Holomorphic Structures Modeled After Compact Hermitian Symmetric Spaces. In: Hano, Ji., Morimoto, A., Murakami, S., Okamoto, K., Ozeki, H. (eds) Manifolds and Lie Groups. Progress in Mathematics, vol 14. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-5987-9_11
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DOI: https://doi.org/10.1007/978-1-4612-5987-9_11
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