A note on inhomogeneous foliations with sections
We give an easy example showing that sections of a singular Riemannian foliation on a simply connected space neither have to be isometric nor injectively immersed.
math.DG↗
arXiv subjects
Stephan Wiesendorf
Publications and source records attributed to Stephan Wiesendorf.
Taut Submanifolds and Foliations
We give an equivalent description of taut submanifolds of complete Riemannian manifolds as exactly those submanifolds whose normal exponential map has the property that every preimage of a point is a union of submanifolds. It turns out that every taut submanifold is also $\mathbb Z_2$-taut. We explicitely construct generalized Bott-Samelson cycles for the critical points of the energy functionals on the path spaces of a taut submanifold which, generically, represent a basis for the $\mathbb Z_2$-cohomology. We also consider singular Riemannian foliations all of whose leaves are taut. Using our characterization of taut submanifolds, we are able to show that tautness of a singular Riemannian foliation is actually a property of the quotient.
math.DG↗