On invariance and Ricci-flatness of Hermitian metrics on open manifolds | Zendy

Bert Koehler | Zendy; Marco Kühnel | Zendy

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On invariance and Ricci-flatness of Hermitian metrics on open manifolds

Author(s) -

Bert Koehler,

Marco Kühnel

Publication year - 2006

Publication title -

commentarii mathematici helvetici

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.603

H-Index - 46

eISSN - 1420-8946

pISSN - 0010-2571

DOI - 10.4171/cmh/63

Subject(s) - mathematics , pure mathematics , divisor (algebraic geometry) , hermitian manifold , invariant (physics) , homogeneous , triviality , manifold (fluid mechanics) , hermitian matrix , flatness (cosmology) , metric (unit) , ricci flat manifold , complex dimension , hermitian symmetric space , lie group , ricci curvature , kähler manifold , combinatorics , mathematical physics , scalar curvature , geometry , physics , curvature , cosmology , mechanical engineering , operations management , quantum mechanics , economics , engineering

We discuss a technique to construct Ricci-flat hermitian metrics oncomplements of (some) anticanonical divisors of almost homogeneous manifoldsand discuss when this metric is complete and K\"ahler. This construction has astrong interplay with invariance groups of the same dimension as the manifoldacting with an open orbit. Lie groups of this type we call divisorial. As anapplication we can describe compact manifolds admitting a divisoriallyinvariant K\"ahler metric on an open subset. Finally, we see a connectionbetween the reducibility of the anticanonical divisor and the non-triviality ofthe K\"ahler cone on the complement.

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