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a e G abelian abelian differentials assume automorphism Borel set characteristic Clifford system compact connected compute contains converges Corollary corresponding countable defined Definition denote diffeomorphism differentiable actions dimension divisor element éléments epimorphism equations euclidean spaces exists exponential map extension fact filter finite follows formula function geodesic group G Hence homology homomorphism identity implies integral invariant irreducible isomorphism isotropy subgroups lattice Lemma lemme Let G Lie algebra Lie group linear Math matrix maximal metric minimal surface Moreover multiplicative non-trivial normal subgroup notation obtain period matrix principal isotropy subgroups principal orbit types proof of Theorem Proposition prove representation resp Riemann surface riemannian satisfies self-adjoint operator semi-simple sequence smooth SO(n solvmanifold sous-groupe subgroup of G subset Suppose Theorem theta constants topology trivial unipotent unique vector field zero