A NOTE ON EXTRINSIC FRAME HOMOGENEITY OF HYPERQUADRICS

Abstract

Let p_i and q_i belong to a hyperquadric Q and (\(e_{1_{i}}\),...,\(e_{n_{i}}\)) and (\(f_{1_{i}}\),...,\(f_{n_{i}}\)) be orthonormal frames in T_piQ and T_qiQ, respectively, where 1 ≤ i ≤ m.  We study sufficient and necessary conditions for existence of an isometry φ : \(\mathbb{R}_{ν}^{n+1} \longrightarrow \mathbb{R}_{ν}^{n+1}\) such that φ(Q) ⊂ Q, φ(p_i) = q_i and dφ(\(e_{j_{i}}\)) =\(f_{j_{i}}\).