On Some Integral Invariants, Lefschetz Numbers and Induction Maps

Futaki, Akito; Tsuboi, Kenji

doi:10.3836/tjm/1270133974

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“…One can see that the function µ on L extends over the 0-section and the oosection to give a C 00 function on M. In fact,µ: In §2, we showed that F appears as one of the G-invariant polynomials F,J,-These G-invariant polynomials are related to the classical invariants such as the equivariant cohomology, the Lefschetz numbers and the Chern-Simons invariants (see e.g. [2], [13], [10], [32], [33], [30]).…”

Section: Drmentioning

confidence: 99%

Einstein–Kähler Metrics with Positive Ricci Curvature

Futaki

Mabuchi²,

Sakane³

Advanced Studies in Pure Mathematics

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and the character :F §4. Chern-Simons invariants and the group lifting of :F Ricci-Positive Case §5. The uniqueness theorem §6. Existence of Einstein-Kahler metrics I §7. Existence of Einstein-Kahler metrics II & Appendix 13 §1. Matsushima's obstru.ction and Kobayashi's semistability Let M be a compact complex connected m-dimensional manifold endowed with a Kahler form w. We then write w in the form where (z1, z2, ... , zm) is a system of holomorphic local coordinates on M. Denote by I: Ra/3 dza ® dzt3 the Ricci tensor of the Kahler form w. Then the associated Ricci form satisfies Ric(w) = H88logdet(gaf3) and represents the de Rham cohomology class 2?rc1 (M)R. Define the corresponding scalar curvature a-( w) and Laplacian Q, by a-(w) := L gt3a Ra/3• a,{3 -82 •-" {3a .-~9 _a_a_a_/3=, a,{3 Z Z 14 A. Futaki, T. Mabuchi and Y. Sakane Now, let G be the group Aut{M) of holomorphic automorphisms of M, and g the corresponding complex Lie algebra H 0 (M,O(TM)). More-Ricci-Positive Case 31 (1978), 339-411.

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Section: Drmentioning

confidence: 99%