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Symmetries and Kähler-Einstein metrics

Claudio Arezzo, Alessandro Ghigi (2005)

Bollettino dell'Unione Matematica Italiana

We consider Fano manifolds M that admit a collection of finite automorphism groups G 1 , ... , G k , such that the quotients M / G i are smooth Fano manifolds possessing a Kähler-Einstein metric. Under some numerical and smoothness assumptions on the ramification divisors, we prove that M admits a Kähler-Einstein metric too.

Symmetries of connections on fibered manifolds

Alexandr Vondra (1994)

Archivum Mathematicum

The (infinitesimal) symmetries of first and second-order partial differential equations represented by connections on fibered manifolds are studied within the framework of certain “strong horizontal“ structures closely related to the equations in question. The classification and global description of the symmetries is presented by means of some natural compatible structures, eġḃy vertical prolongations of connections.

Symmetrization of brace algebra

Daily, Marilyn, Lada, Tom (2006)

Proceedings of the 25th Winter School "Geometry and Physics"

Summary: We show that the symmetrization of a brace algebra structure yields the structure of a symmetric brace algebra. We also show that the symmetrization of the natural brace structure on k 1 Hom ( V k , V ) coincides with the natural symmetric brace structure on k 1 Hom ( V k , V ) a s , the direct sum of spaces of antisymmetric maps V k V .

Symmetry problems 2

N. S. Hoang, A. G. Ramm (2009)

Annales Polonici Mathematici

Some symmetry problems are formulated and solved. New simple proofs are given for some symmetry problems studied earlier. One of the results is as follows: if a single-layer potential of a surface, homeomorphic to a sphere, with a constant charge density, is equal to c/|x| for all sufficiently large |x|, where c > 0 is a constant, then the surface is a sphere.

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