Tammela, P. P. Two remarks on Bravais manifolds. (Russian) Zbl 0374.10022 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 33, 90-93 (1973). Let \(G\) be a finite group of integral-valued unimodular matrices of order \(n\). The set \(B_G\) of all quadratic forms \(f(x)\) for which each element of the group \(G\) is an automorphism is called the Bravais manifold of the group \(G\). The following two theorems are proved: (1) Let \(G\) be defined as above, \(G\not\subset \{\pm I_n\}\) (the unit matrix of order \(n\)), then \(\dim B_G \le N - (n - 1)\) and this bound is actually attained. (2) Let \(B_{G\varphi}\) be the Bravais manifold of the group of automorphisms \(G_\varphi\) of a given perfect form \(\varphi\). If \(\varphi\) is not extreme, then \(\dim B_{G\varphi} > 1\). Reviewer: Olaf Ninnemann (Berlin) Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 2 Documents MSC: 11H55 Quadratic forms (reduction theory, extreme forms, etc.) 11H06 Lattices and convex bodies (number-theoretic aspects) Keywords:finite group of integral-valued unimodular matrices; quadratic forms; Bravais manifold; group of automorphisms PDFBibTeX XMLCite \textit{P. P. Tammela}, Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 33, 90--93 (1973; Zbl 0374.10022) Full Text: EuDML