Open Access
March 2014 Taut submanifolds and foliations
Stephan Wiesendorf
J. Differential Geom. 96(3): 457-505 (March 2014). DOI: 10.4310/jdg/1395321847


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 explicitly construct generalized Bott-Samelson cycles for the critical points of the energy functionals on the path spaces of a taut submanifold that, 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.


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Stephan Wiesendorf. "Taut submanifolds and foliations." J. Differential Geom. 96 (3) 457 - 505, March 2014.


Published: March 2014
First available in Project Euclid: 20 March 2014

zbMATH: 1302.53032
MathSciNet: MR3189462
Digital Object Identifier: 10.4310/jdg/1395321847

Rights: Copyright © 2014 Lehigh University

Vol.96 • No. 3 • March 2014
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