Hamiltonian homogeneity on a complex contact manifold

The notion of c-manifolds is introduced as a generalization of complex contact manifolds as well as the degree of symplectifications. And the condition of infinitesimal Hamiltonian homogeneity on a c-manifold is established by means of a moment map defined on the symplectification.Comment: 26 pages; v4: major conceptual changes from v3 by deleting the section 3 because Theorem 3.2 (ii) is wrong

Orbit decomposition of Jordan matrix algebras of order three under the automorphism groups

The orbit decomposition is given under the automorphism group on the real split Jordan algebra of all hermitian matrices of order three corresponding to any real split composition algebra, or the automorphism group on the complexification, explicitly, in terms of the cross product of H. Freudenthal and the characteristic polynomial.Comment: v2, 32 pages, presentation improved, minor errors corrected, and the title changed as appeared in J. Math. Sci. Univ. Toky

From Homma's theorem to Pick's theorem

From Homma’s PL Gauss-Bonnet theorem applied on a PL-complex in a plane, many generalizations of Pick’s theorem on a lattice PL-figure are obtained in a unified geometric way