关于SL_2（C）/Γ中的椭圆曲线、Schanuel猜想和测地线长度
On Elliptic Curves in SL_2(C)/Γ, Schanuel's conjecture and geodesic lengths
摘要：
设H是SL_2（C）的离散余紧子群.我们猜想商流形X=SL_2（C）/H包含无穷多条非齐次的椭圆曲线，并证明了如果Schanuel猜想成立，情况确实如此.在H与SL_2（R）的交在SL_2（R）中是余紧的特殊情况下，我们也证明了这一点。此外，我们推导出实双曲2-和3-折叠的测地长度谱的一些结果。
英文摘要：
Let H be a discrete cocompact subgroup of SL_2(C). We conjecture that the quotient manifold X=SL_2(C)/H contains infinitely many non-isogeneous elliptic curves and prove that this is indeed the case if Schanuel's conjecture holds. We also prove it in the special case where the intersection of H and SL_2(R) is cocompact in SL_2(R). Furthermore, we deduce some consequences for the geodesic length spectra of real hyperbolic 2- and 3-folds.
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