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First Laplace eigenvalue of strongly isotropy irreducible spaces

Differential Geometry 2025-11-19 v1 Spectral Theory

Abstract

We study the smallest positive eigenvalue λ1\lambda_1 of the Laplace-Beltrami operator associated with any compact strongly isotropy irreducible space. We provide an explicit expression for all simply connected cases. Furthermore, every strongly isotropy irreducible space is automatically an Einstein manifold, and we prove for each of them that E<λ116EE<\lambda_1\leq 16E, where EE denotes the corresponding Einstein constant.

Keywords

Cite

@article{arxiv.2511.14463,
  title  = {First Laplace eigenvalue of strongly isotropy irreducible spaces},
  author = {Emilio A. Lauret and Fiorela Rossi Bertone and Alejandro Tolcachier},
  journal= {arXiv preprint arXiv:2511.14463},
  year   = {2025}
}