On the Validity or Failure of Gap Rigidity for Certain pairs of Bounded Symmetric Domains

Details On the Validity or Failure of Gap Rigidity for Certain pairs of Bounded Symmetric Domains On the Validity or Failure of Gap Rigidity for Certain pairs of Bounded Symmetric Domains

2004-03-16

arxiv.org/abs/math/0403270v1

Mathematics

Algebraic Geometry

33 pages

Scientific paper

In our previous work "Characterization of certain homorphic geodesic cycles on Hermitian locally symmetric manifolds of the noncompact type" in "Modern methods in Complex Analysis" Annals of Math. Studies 138 (1995) 85-118, we formulated a conjecture: the so called "gap phenomenon". The purpose of the article is two-fold. We give a counterexample to the gap phenomenon in the most general situation. We give new examples of situations in which the gap phenomenon holds and a unified conceptual, hopefully definitive, presentation of these situations. In the last section of the article, we survey some open problems connected to the gap phenomenon.

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