TY - JOUR AU - H. J. Rivertz PY - 2009/12/25 Y2 - 2024/03/29 TI - On an invariant on isometric immersions into spaces of constant sectional curvature JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 61 IS - 12 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/3129 AB - In the present paper, we give an invariant on isometric immersions into spaces of constant sectional curvature. This invariant is a direct consequence of the Gauss equation and the Codazzi equation of isometric immersions. We apply this invariant on some examples. Further, we apply it to codimension 1 local isometric immersions of 2-step nilpotent Lie groups with arbitrary leftinvariant Riemannian metric into spaces of constant nonpositive sectional curvature. We also consider the more general class, namely, three-dimensional Lie groups $G$ with nontrivial center and with arbitrary left-invariant metric. We show that if the metric of $G$ is not symmetric, then there are no local isometric immersions of $G$ into $Q_{c^4}$. ER -