February 2023 Aq-components of geometric classes in compact Hermitian locally symmetric spaces
Arghya Mondal
Author Affiliations +
Kyoto J. Math. 63(1): 51-66 (February 2023). DOI: 10.1215/21562261-2022-0031

Abstract

Let ΓGK be a compact Hermitian locally symmetric space, where G is simple. We study the components of a de Rham cohomology class of ΓGK with respect to the Matsushima decomposition, where the class is obtained by taking the Poincaré dual of a totally geodesic complex analytic submanifold. Using an improved version of the vanishing result of Kobayashi and Oda, we specify the existence of certain components of such cohomology classes when G=SU(p,q).

Citation

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Arghya Mondal. "Aq-components of geometric classes in compact Hermitian locally symmetric spaces." Kyoto J. Math. 63 (1) 51 - 66, February 2023. https://doi.org/10.1215/21562261-2022-0031

Information

Received: 3 January 2019; Revised: 3 November 2020; Accepted: 22 February 2021; Published: February 2023
First available in Project Euclid: 29 November 2022

MathSciNet: MR4593188
zbMATH: 07655222
Digital Object Identifier: 10.1215/21562261-2022-0031

Subjects:
Primary: 22E40
Secondary: 11F67

Keywords: Automorphic representations , geometric cycles , vanishing theorem

Rights: Copyright © 2023 by Kyoto University

Vol.63 • No. 1 • February 2023
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