On the validity or failure of gap rigidity for certain pairs of bounded symmetric domains

DOI10.4310/AJM.2004.V8.N4.A24zbMATH Open1085.32010arXivmath/0403270WikidataQ125833260 ScholiaQ125833260MaRDI QIDQ2484141

Ngaiming Mok, Philippe Eyssidieux

Publication date: 3 August 2005

Published in: The Asian Journal of Mathematics (Search for Journal in Brave)

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/math/0403270

zbMATH Keywords

gap rigidityholomorphic geodesic cyclesemistable point

Mathematics Subject Classification ID

Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15) Period matrices, variation of Hodge structure; degenerations (32G20) Differential geometry of symmetric spaces (53C35)

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