Year: 2026
Type: article
Abstract: In this article, we study closed, positively curved n -manifolds that admit an effective, isometric $${\mathbb {Z}}_{p}^r$$ Z p r -action with a fixed point, where p is an odd prime. For all sufficiently large n , we obtain a symmetry rank bound in Theorem A that improves the approximate 3 n /8 bound of Fang and Rong [7] and Ghazawneh [10]. We improve on this bound for small odd primes $$3\le p\le 19$$ 3 ≤ p ≤ 19 in Theorem B. Two of our main tools come from the theory of error-correcting codes and are of independent interest: we derive a finite-length Plotkin bound and a finite-length Elias-Bassalygo bound for q -ary codes and show that the finite-length Plotkin bound is asymptotically sharper than the corresponding Elias-Bassalygo bound for all primes $$p \ge 23$$ p ≥ 23 .
Source: Journal of Geometric Analysis
Authors: Muhammad Abdullah, Catherine Searle
Institution: Wichita State University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W4415910189
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