Spheres in a Weyl space (Q2733954)

Let \(\overline W_m(\overline g,\overline T)\) be an \(m\)-dimensional Weyl space with a symmetric linear connection \(\overline\nabla\) and a complementary 1-form \(\overline T\) such that \(\overline\nabla\overline g= 2(\overline T \otimes \overline g)\). The authors define an \(n\)-sphere in \(\overline W_m(\overline g,\overline T)\) to be an \(n\)-dimensional umbilical submanifold \(W_n(g,T)\) equipped with a non-zero curvature vector. \(n\)-spheres, \(n\geq 2\), are characterized by using circles, namely, it is proved that \(W_n(g,T)\) is an \(n\)-sphere in \(\overline W_m(\overline g,\overline T)\) if and only if a circle in \(W_n(g,T)\) is a circle in \(\overline W_m(\overline g,\overline T)\).NEWLINENEWLINEFor the entire collection see [Zbl 0966.00031].